School Science Lessons
UNPh26.1
2018-11-09
Please send comments to: J.Elfick@uq.edu.au

26.1.0 Sound, interference

Table of contents

See: Sound, (Commercial)

26.8.0 Interference & diffraction

26.6.0 Musical notes

26.7.0 Reflection & refraction

26.9.0 Sound recording

26.5.0 Speed of sound

26.4.0 Transmission of sound

26.1.0 Wave properties of sound

26.8.0 Interference and diffraction of sound, beats
See: Sound (Commercial)
26.8.1 Beats, superposition of waves of different frequencies
Experiments
26.8.0 Interference and diffraction of sound, beats
2.2.2 Energy transfer between pendulums, by resonance
26.8.2 Interference of sound waves with tuning forks
26.8.8 Interference of two sound sources
26.8.6 Loaded tuning forks
26.8.7 Resonating objects have same frequency as source of vibration
26.9.8 Sound waves extinguish a fire
26.8.3 Superposition of waves of equal frequencies with tuning forks
26.8.4 Superposition of waves of equal frequencies with loudspeakers
26.8.9.1 Two slit interference with microwaves
26.8.9 Ultrasonics, ultrasonic interference
26.8.5 Wave interference in water, drop stones in water

26.6.0 Musical notes, ear and voice, tones
4.101 Ear and hearing
26.3.2.9 Musical instruments
26.3.2.3 Musical scale, tones, sharps and flats, equal temperament scale, musical instruments
Experiments
26.6.10 Attenuation and intensity with a decibel, dB, meter
26.6.11 Attenuation of materials
26.6.6 Bottle sounds
26.6.18 Circular glockenspiel
26.3.2.10 Musical notes, wind instruments
26.6.8 Musical saw
26.3.2.2 Octaves and pitch, sol-fa (solfege) syllabi
26.3.2.11 Pan pipe, panpipe, syrinx, mouth organ
26.6.12 Reverberation time for architectural acoustics
26.6.13 Ripple tank acoustics
26.6.9 Savart wheel
26.6.7 Siren
26.6.1 Tones
9.8.0 Voice and speaking

26.7.0 Reflection and refraction of sound
26.7.0 Reflection and refraction of sound
26.7.3 Balloon as a sound lens, acoustic lens
26.7.2 Echoes in a ripple tank "theatre"
26.7.1 Reflection of sound

26.5.0 Speed of sound (Velocity of sound in gases, liquids, and solids)
Experiments
26.5.0 Speed of sound (Velocity of sound in gases, liquids, and solids)
26.5.01 Sound barrier, sonic barrier
26.7.4 Speed of sound depends on the density of the carrier gas, helium / oxygen mixture
26.3.1.6 Speed of sound in air and frequency of a tuning fork
26.5.6 Speed of sound in liquids
26.5.7 Speed of sound in liquids with bubbles
26.5.5 Speed of sound in solids
37.5.9 Speed of sound, Thunderstorm (See 3.)
26.5.1 Speed of sound with a closed resonance tube
26.5.3 Speed of sound with a drum
26.5.2 Speed of sound with a tuning fork
26.5.4 Speed of sound with echoes
26.5.02 Windshear and noise level, noise of thunder

26.9.0 Sound recording and reproduction, microphone
See: Electrical equipment, Amplifiers, (Commercial)
26.9.0 Analogue and digital recording
Experiments
26.9.3 Cassette recorder
26.9.4 Compact disc, CD
38.5.4 Crystal microphone
38.2.05 Crystal microphone, Earphones, (Electronics)
26.9.7 Glass tube with an open end, using signal generator
29.9.6 Gramophone record, "vinyl"
26.9.2 Microphone and loudspeaker
26.6.21 Microphone and oscilloscope
26.9.01 Telephone carbon microphone, transducer, load cell

26.4.0 Transmission of sound, how sound travels
26.4.0 Transmission of sound
Experiments
26.4.4 Bell from a spoon
26.4.13 Chladni vibrating plate
26.4.20 Comb kazoo
26.4.18 Goose horn tube
1.16 Hearing sounds game (Primary)
4.7 How sound travels (Primary)
26.4.19 Kazoo tube
1.7 Knocking sounds (Primary)
26.4.12 Kundt's tube
26.4.8 Listen to a fork
26.4.6 Materials that absorb sound
26.4.1 Sound waves cannot travel through a vacuum
26.4.9 Sound waves extinguish a candle flame
26.4.5 Sound waves travel in straight lines
26.4.2 Sound waves travel through an air column, stethoscope
26.4.7 Sound waves travel through wood
26.4.10 Sound waves travel through a cylinder
26.4.11 Sound travels along a wire fence
26.4.14 Sound waves patterns
26.4.15 Wave patterns of a tuning fork.

26.1.0 Wave properties of sound, oscillation, vibration
See: Waves (Commercial)
See diagram 25.2.2: Particles in a longitudinal wave
Oscillation
Oscillation is typically a swing to and fro in a regular rhythm, e.g. the swing of a pendulum, the "tick tock" of a clock, a part of a machine.
So during an oscillation a definite distance is covered by the movement about its equilibrium position.
However, "the oscillation" describes the movement of a body from its resting place to the maximum distance it can cover on one side to
the maximum distance on the other side and back to its resting place.
That maximum distance is called the amplitude or maximum displacement.
During oscillation the body takes a fixed time to complete one
oscillation called periodic movement.
The time taken to complete one oscillation is its frequency.
An oscillating electric current has periodic reversal of direction.

Vibration
Vibration of a body is the movement of the body about its mean position, as with oscillation, but the movement can be linear, circular,
periodic or non periodic.
So the movement of vibration can be in all directions, e.g. Vibration occurs when a string is plucked.
Sound vibration is caused by a rapid alternation about an equilibrium position of the particles of an elastic body which is transmitted to
air molecules.
A vibration damper restricts or stops vibrations, e.g. in a piano, horn mute.
Vibrating sources of sound produce a series of alternate compression and rarefaction that can travel as a longitudinal wave through
a medium, e.g. air, water, wood, but not through a vacuum.
The particles of the medium vibrate forwards and backwards in the same directions as the wave is travelling.
For example, a loudspeaker cone vibrates forwards to produce a compression, "thicker air", and backwards to produce a rarefaction,
"thinner air".

Sound wave
A sound wave is the mechanical wave motion when sound energy travels through a medium.
Sound waves are compression waves in a material medium such as air, water, or steel.
When the compression and rarefaction of the waves strike the eardrum, causing it to vibrate, which results in the sensation of sound,
provided the frequency of the waves is between about 20 Hz and 20 000 Hz.
Waves with frequencies above 20 kHz are called ultrasonic waves.
Those with frequencies below 20 Hz are called infrasonic waves.
The word "sound" refers to the sensation when the eardrum reaction to vibrations.
Sound waves require vibration of the molecules or particles of their medium.
Sound is a longitudinal wave motion and will not pass through an evacuated space.
Sound travels as a wave in which motion the movement of the particles is transmitted but not the physical particles themselves.
In a transverse wave the particles oscillate perpendicular to the direction of the wave.
Sound waves are longitudinal waves so the particles oscillate parallel to the wave's direction of wave travel.
Sound waves have a length, amplitude and frequency.

Wavelength
Wavelength is the distance from one part of one wave to the same place on the next wave, e.g. the distance from the place of
maximum compression to the next place of maximum compression.

Amplitude
Amplitude is the difference between the pressure in the compression or the minimum pressure in the rarefaction and the pressure of
the normal undisturbed air.

Frequency
Frequency refers to how often a rarefaction/compression pair pass a given point in a second, e.g. a tuning fork for the A above
middle C vibrates 440 times every second or at 440 Hz.
Frequency, f, is the number of compressions per second.
The distance between compressions is the wavelength.
Speed = frequency × wavelength.

26.3.2.11 Pan pipe, panpipe, syrinx, mouth organ
Sound science, Sarah Tulga, See: Instruments, panpipes (internet)
See diagram 26.3.01 Standing waves in air columns, See: Air column closed at one end
The air column inside the pipe may generate standing waves so that the pipe emits a harmonious sound.
Experiment
Make drinking straw panpipes.
Cut a strip of corrugated cardboard about 60 mm wide and 150 mm long so that the corrugations run along the short distance.
Push a straw through every second opening of the cardboard.
Cut each straw to a different length, the longest at one end and the shortest at the other, with even changes of length in between.
Blow across the tops of the straws to make a sound.
Tune the instrument by cutting the length of each straw so that a musical note can be played

26.4.0 Transmission of sound
Echo, absorption, transmission, string telephone, sound insulation, soundproofing, acoustics, baffles
When a periodic disturbance occurs in air, longitudinal sound waves spread out from it in three dimensions, just like the water waves
that spread out from a vibrating source in two dimensions.
The air in the path of a sound wave becomes alternately denser and rarer.
These changes in pressure cause your eardrums to vibrate with the same frequency to produce the sensation of sound.
The speed of sound in air is 332 m / sec at 0oC.
The speed of sound increases by about 0.2% for each 1oC rise in air temperature.

26.4.1 Sound waves cannot travel through a vacuum
See: Vacuum, (Commercial)
The speed of sound in air at 0oC = 331 ms -1.
1. Use an aspirator or simple vacuum pump to pump the air from a bell jar fitted with a spigot or a large round bottom flask.
Use a bicycle pump to make a simple vacuum pump.
Open the pump and remove the piston.
Unscrew the bolt that holds the leather washers then reverse the washers by turning them over.
Replace the washers on the piston and reinsert the piston in the pump cylinder.
Suspend a small bell from fine threads inside the jar or bottle and shake the bell while the jar is filled with air.
You can hear the bell ringing quite clearly.
Use the aspirator or simple air pump to remove as much air as possible from the jar.
Shake the bell again.
The sound of the bell is not as loud as before because sound cannot travel through a vacuum.
Repeat the experiment with a loud ticking watch, electric bell or metronome.
2. Use a large wide mouthed bottle with a rubber stopper.
Drill a hole on the stopper and insert a short glass tube into the hole.
Use a small radio.
Turn on the radio and turn up the volume to the maximum.
Open the bottle and put the ratio into it.
Cover the bottle with its stopper again and connect the glass tube on the stopper to an air pump with a rubber tube.
Fill the seaming with some oil.
Draw the air out of the bottle and listen to the sound from the radio at the same time.
The sound is silent, soft and loud.
If there is a fit screw clamp, nip the rubber tube with the clamp before drawing out the air.
Repeat the experiment screwing the clamp tightly after drawing the air out of the bottle and using the clamp to control the speed at
which air enters into the bottle after removing the air pump from the rubber tube.
The process of sound's change may be displayed more obviously.
If no fit radio, tie a small bell to a piece of very short string then put
the bell into the bottle.
Make sure that the length of the string is fit so that the bell does not touch the wall of the bottle when shake the bottle.
Repeat the experiment shaking the bottle.
You may see the bell waggling but you may not hear the sound from the bell firstly and gradually you may hear the sound and finally the
sound recovers completely.
3. Fit a round bottom flask with a one-hole stopper.
Insert a glass tube through the one-hole stopper.
Use a Bunsen burner to bend one end of the glass tube.
Attach rubber tubing to the other outer end of the glass tube.
Attach a clip to the rubber tubing.
Use a light thread to suspend a metal tube from the bent end of the glass tube.
Insert a long wire to the underside of the stopper so that it can knock against the metal tube acting as a bell.
Put water in the flask.
Insert the stopper into the flask and shake the flask to hear the sound of the wire knocker hitting the tubular bell.
Boil the water in the flask until all the air is driven out by the escaping steam then close the clip around the rubber tube.
Shake the flask again .to hear the sound of the wire knocker hitting the tubular bell.
Much less or no sound is heard.

26.4.2 Sound waves travels through an air column, stethoscope
See: Sound, Stethoscope, (Commercial)
1. Put the end of the handle of a funnel into your ear.
Be careful not to harm your eardrum.
Listen to the every sound in the classroom.
You may hear various sounds even whispers between students.
Use a PVC tube of length about 50 cm.
Insert the tube into a small funnel.
It may be used as a simple stethoscope.
Press one end of the tube close to your ear and place the funnel on a mechanical watch.
You may hear the "tick tick" sound the watch emits clearly.
Bend the above PVC tube slightly then put it on your chest.
You may hear your heart's palpitation.
Here the stethoscope made by you has the same principle with that doctors use.
Through stethoscopes doctors listen attentively to palpitations, breaths and any sounds patients' chest emit.
2. Fit the plastic tube over the small opening of the funnel.
Place the large opening of the funnel over your heart or stomach and listen in at the other end of the plastic tube.
See how many different body sounds you can identify from inside your body.

26.4.4 Bell from a spoon, ringing spoon
See diagram 26.192: Bell from a spoon
1. Tie the middle of one metre of string around a fork.
Tie each end of the string around the index fingers.
Press the ends of the string into the ears with the fingertips and let the spoon hang down loosely.
Note the different sounds when the spoon swings and hits different objects, e.g. wooden table, glass window, iron pot.
Hit the spoon with another spoon and hear a chime like a bell.
Sound waves travel along the string to the ears.
2. To compare sound's travelling along solid and in air, tie a stainless steel spoon to the midpoint of a string of length about 1 m.
Insert the two ends of the string into your ears.
Bend to make the spoon overhang free.
Shake the string to knock a metallic object or let other person to knock the spoon with a metallic object.
Listen the sound along the string.
Knock again after leaving the ends of the string off your ears.
Compare the sounds.
Press your ear close to a tabletop then knock the table.
Listen to the sound through the table.
Leave your ear off the tabletop then knock the table again.
Listen the sound from the air.
Describe the difference between the sounds.
Record your sound on a tape then play it.
You may find that it is different from your ordinary sound.
If you record other people's sounds then play them, the effects are the same.
Discuss the reason.
When the sound travels in different medium, the difference in speed and energy of the sound is remarkable.
The speed and loudness of sound is much greater in solid than in air.
3. Use a 1 metre long string.
Tie the middle of it around the handles of 4 to 5 spoons so that when you hold up the two ends of the string the spoons bang on each
other.
Push the ends of the sting into your ears, shake your head, and hear the chimes.
The larger the spoon the lower pitch the sound.
Use fine wire instead of string to get a clearer sound.
Spoons are curved like bells.

26.4.5 Sound waves travel in straight lines
In a piece of poster board or construction paper, cut a strip out about 20 cm wide and 1 m to a paper tube.
Place a clock at one end of the paper tube.
Through another end of the paper tube listen to the "tick tick" the clock emits.
It is clearer than in air.
It shows that sound travels along straight lines.

26.4.6 Materials that absorb sound
Test the sound absorbing properties of small pieces of material, e.g. rubber, sponge, felt.
Place the piece of material on a wooden table top, strike a tuning fork, and bring the handle down on it.
Then strike the tuning fork again and touch its handle on the wooden table top.
Note which sound is louder.
Test each material.

26.4.7 Sound waves travel through wood
To show that sound waves travel through wood, rest the ear against one end of a table top and gently tap the other end of the table
with a ruler or pencil.

26.4.8 Listen to a fork
Tie a fork in the middle of a piece of string about a yard long.
Wind the ends several times around your forefingers and hold the tips of your fingers in your ears.
Let the fork strike a hard object.
If the string is then stretched, you will hear a loud, bell like peal.
The metal vibrates like a tuning fork when it strikes the hard object.
The vibration is not carried through the air in this case, but through the string, and the finger conducts it directly to the eardrum.
Tie a fork in the middle of a piece of string about a yard long.
Wind the ends several times around your forefingers and hold the tips of your fingers in your ears.
Let the fork strike a hard object.
If the string is then stretched, you will hear a loud, bell like peal.
The metal vibrates like a tuning fork when it strikes the hard object.
The vibration is not carried through the air in this case, but through the string, and the finger conducts it directly to the eardrum.

26.4.9 Sound waves extinguish a candle flame
Cut the base off a plastic drink bottle.
Stretch a thin sheet of plastic or rubber over the cut base and secure it with an elastic band around the base.
Light a small birthday cake candle.
Hold the opening of the plastic drink bottle near the lighted candle.
Strongly tap the plastic sheet at the other end.
The vibration can extinguish the flame.

26.4.10 Sound waves travel through a cylinder
Hold a ticking watch to your ear.
Then move it further and further away until you can just no longer hear it.
Note the distance between the watch and your ear when you can no longer hear it.
Make a cylindrical roll of paper about the same distance in length.
Hold the paper cylinder to your ear then hold the ticking watch at the end of the roll of paper.
You can now hear the watch ticking.
When you first heard the watch ticking vibrations travelled out from the watch in all directions.
When sound vibrations were trapped in the roll of paper they could not move in all directions, saved some energy and so the vibration
move a longer distance through the cylindrical roll.

26.4.11 Sound waves travels along a wire fence
Divide into two groups and position yourselves as far apart as possible along a wire fence so you can still see the other group.
Watch the other group strike the wire.
Time how long it takes for the sound to reach you in the air.
Now place you ear on the wire of the fence and listen and time it again.
If a long enough fence is not available listen to faint sounds travelling through a table or other solid object.
You can hear sounds through the table that you may not hear through the air since the sound is travelling faster and therefore does not
die out in as short a distance.

26.4.12 Kundt's tube
See: Resonance, Kundt's tube, (Commercial)
See: Waves (Kundt's apparatus), (Commercial)
Show the characteristic modes standing waves in a closed plastic pipe with cork dust.
Experiment
1. Sprinkle fine dry cork dust in the horizontal plastic pipe.
Place the Kundt's Tube apparatus on an overhead projector with a loudspeaker next to the opening of the plastic pipe.
Adjust the frequency of a loudspeaker.
The cork dust forms recurring patterns when the radio signal excites the column of air in the plastic tube at one of the standing wave
frequencies.

2. See diagram 25.1.3.1: Kundt's Tube apparatus
A glass tube holds a metal rod with a metal disk attached to one end.
A stopper closes the other end of the tube.
Velocity of a wave, v = fl, where f = frequency and l = wavelength.
When the rod is stroked, standing waves are set up in the vibrating rod.
The rod is clamped at its centre so this point is a node of zero amplitude of motion and the ends of the rod that are free to vibrate are
antinodes, i.e. maximum amplitude of particles' motion along the direction of the rod.
When the rod is vibrating in this manner it is vibrating with its fundamental frequency and the wavelength of the standing wave is twice
the length of the rod.
Place a thin layer of dry cork dust inside the tube.
Clamp the rod at its centre.
Position the disk on the end of the rod within the tube.
Place rosin on leather cloth, grip the rod and pull toward the end to set the rod into longitudinal vibrations and produce a high pitch
note.
Cork dust heaps form in the tube.
Record the average distance between dust heaps.
Twice this value is the wave length of the sound.

26.4.13 Chladni vibrating plate
See diagram 26.4.13: Chladni vibrating plate apparatus
Show the vibration modes of thin plates with Chladni figures.
Experiment
Clamp the Chladni vibrating plate on to a trolley.
Sprinkle fine dry salt evenly over the whole plate.
Make a "violin bow" from a hacksaw frame and fishing line.
Draw the violin bow across the plate to cause vibration.
Try to achieve distinct nodal patterns of the salt.

26.4.14 Sound waves patterns
See diagram 26.190: Sound wave patterns
The number of complete vibrations in one second is the frequency of a particular vibration.
The way in which different sound frequencies combine is analogous to water waves.
Ocean waves are longest, i.e. of low frequency.
Let a small motorboat pass over these waves.
The boat sends out its own waves, which have a higher frequency than ocean waves.
Wind will make tiny ripples across the surface of the motorboat waves.
The last ripples usually have an even higher frequency than the other two.
These three vibrations can combine to form a pattern.

26.4.15 Wave patterns of a tuning fork
See diagram 26.191: Wave patterns of a tuning fork
Use hot wax to attach a piece of fine wire to the prong of a tuning fork.
Hold the fork rigidly by the handle and horizontally just above the table top.
Use a candle to smoke a piece of glass.
Lay the smoked glass under the prong with the fine wire bent to touch the glass.
Start the tuning fork vibrations with the finger and move the glass along the table fast enough to make a wavy line on it.
Repeat this experiment by moving the glass at different speeds and using different tuning forks.
Note the markings on the tuning forks, e.g. "C", and compare the wave patterns.

26.4.18 Goose horn tube
See diagram 26.193: Goose horn tube
Cut a 10 cm X 10 cm square of thin cardboard with a 1 cm X 1 cm tab at one corner.
Roll the cardboard into a tube leaving the end where the tab is until last.
Bend the tab over the end of the tube.
The tab must completely cover the open end of the tube so you may have to roll the tube again more tightly.
Use adhesive tape to secure the tube.
Suck on the end of the tube away from the tab.
The tab makes a noise like a goose when it vibrates against the end of the tube.
Some people can also put the end of the tube with the tab inside the mouth and produce a sound by blowing into the tube.

26.4.19 Kazoo tube
See diagram 26.193: Kazoo tube
Use a large cardboard tube, e.g. a post office mailing tube.
Cut a square of waxed paper large enough to be wrapped around the end of the tube.
Secure the waxed paper with a thick rubber band.
Make a hole in the side of the tube about 4 cm from the covered end.
Press the open end of the tube around your mouth and make a humming noise or say "doing, doing".
The quality of the sound is changed by the vibrating membrane so this instrument can be called a membranophone.
Repeat the experiment with kitchen aluminium foil instead of waxed paper.

26.4.20 Comb kazoo
Hold a straight hair comb with the teeth pointing downwards.
Cut out a piece of waxed paper twice the area of the comb.
Fold the piece of waxed paper into two and place it over the comb so that each side is covered.
While holding the waxed paper against the comb use it to touch your lips while you make a "oo, oo, oo" sound.
The waxed paper vibrate to change the original sound and cause a tingling sensation in your lips.

26.5.0 Speed of sound
See: Waves (Kundt's apparatus), (Commercial)
1. The speed of sound in air at room temperature, 20oC, v = 343 m /s.
As temperature of air increases, the molecules in air move faster, so the speed of sound increases with temperature.
The speed of sound is independent of pressure, frequency, and wavelength but is proportional to the square root of the absolute
(Kelvin) temperature.
The speed increases with temperature by about 0.61 m / s for each 1oC rise.
So speed of sound in air at 0o C = 331 m / s.
2. The speed of sound is faster in solids than liquids than gases, because the speed of sound through a material is related to the elasticity
and density of the material.
For example speed of sound at 0oC of fresh water = 1 410 m / s, sea water = 1 540 m /s, wood 3 850 m /s, and steel 5960 m / s.
The speed of sound also increases with the intensity of the source, e.g. explosions.
3. The speed of sound can be measured by time of transmission between two amplifiers, time measurement replaced by a measurement
of the inverse of time (frequency), v = fλ.
3.1 Kundt's tube is used to measure the speed of sound in any gas.
It a powder to make the nodes and antinodes visible to the human eye.
3.2 If a tuning fork is held near the mouth of a long pipe dipping into water.
The pipe will resonate if the length of the air column in the pipe is equal to ({1+2n}λ/4) where n is an integer.
The antinodal point for the pipe at the open end is slightly outside the mouth of the pipe so find two or more points of resonance and
measure half a wavelength between these.

26.5.01 Sound barrier, sonic barrier
7. When the speed of a source equals the speed of sound the wave fronts cannot escape the source.
The wave form a large amplitude "sound barrier" that makes flight difficult.
The term "sound barrier" or "sonic barrier" was used when pilots doing high speed dives noticed that as flying speeds approached the
speed of sound: aerodynamic drag increased unusually and lift and manoeuvrability decreased.
When the speed of a source exceeds the speed of sound, the wave fronts lag behind the source in a cone-shaped region with the
source at the vertex.
The edge of the cone forms a supersonic wave front with an unusually large amplitude called a "shock wave".
The shock wave is heard as a "sonic boom".
Unlike ordinary sound waves, the speed of a shock wave varies with its amplitude.
The speed of a shock wave is always greater than the speed of sound in the fluid and decreases as the amplitude of the wave decreases.
When the shock wave speed equals the normal speed, the shock wave is reduced to an ordinary sound wave.
The ratio of the speed of a moving object, v, to the speed of sound, c, in a fluid is called the Mach number in honour of Ernst Mach,
1838-1916.
Mach 0.5 is half the speed of sound and Mach 2 is twice the speed of sound.
Subsonic speeds have a Mach number between zero and one.
Supersonic speeds have Mach numbers greater than one.
The shock wave from a supersonic object is a cone composed of overlapping spherical wave fronts.

26.5.02 Windshear and noise level, noise of thunder
Windshear (wind shear, wind gradient), refers to the lower wind speed near the ground because of friction with objects on the ground
and uneven ground.
The wind velocity gradient tends to bend sound waves downward when moving in the same direction of the wind and upwards when
moving against the wind.
If sound is moving faster at a height above the ground than at ground level, then the sound wave is bent towards the ground.
This refraction causes noise increase downwind and noise decrease upwind.
The noise of road traffic is greater if the wind is blowing in the direction of from the traffic towards you, and vice versa.
So the wind itself does not increase of decrease the speed of sound.
As acoustic waves moving in the direction of wind are refracted downwards, audibility in the direction of the wind is increased.
A coastal foghorn may be heard a long way out to sea during offshore winds, but be heard only at a short distance during onshore
winds.
The noise of thunder may not be heard at a distance greater than 25 km causing "the calm before the storm".
However, another factor here is that the speed of sound is proportional to the square root of temperature, so by Snell's law sound
waves are refracted upwards.
So given a typical lapse rate of 7.5 oK per km, from a height of 4 km the maximum audibility is 25 km.
In aviation, windshear is a generic term referring to any rapidly changing wind currents.
Local, short-lived downdrafts called "microbursts" radiate outward as they rush toward the ground from a cloud, creating an increasing
headwind over the wings of an aircraft.
This headwind causes a sudden leap in airspeed, so the aircraft lifts.
Inexperienced pilots are likely to react by reducing engine power.
However, as the plane passes through the shear, the wind quickly becomes a downdraft and then a tailwind.
The extra lift and speed vanish so the aeroplane suddenly loses airspeed and altitude because it now flying on reduced power.
So the pilot must increase power to the engines to avoid a crash.
Many air accidents are caused by this phenomenon.

26.5.1 Speed of sound with a closed resonance tube
See diagram 26.3.01: Closed resonance tube
Measure the diameter of the resonance tube.
Add water to the glass cylinder until 3 / 4 full.
Hold the resonance tube vertically in the cylinder with one end in the water so the water seals one end of the tube.
You can raise and lower the tube to vary the length of the air column in the tube.
Strike the tuning fork with a rubber bung.
Hold the vibrating tuning fork horizontally close to the open end of the tube.
Move the tube and tuning fork up and down until the sound is best reinforced.
If you find more than one position where reinforcement occurs move the tube up and down to find the shortest tube length that gives the
loudest sound.
Hold the tube in the position of best sound reinforcement and measure the distance L from the top of the resonance tube to the water.
The length of the air column must be increased by 0.4 × diameter of the tube to correct for the air outside the top of the tube that
vibrates with the air column in the tube.
The corrected length of the air column = 0.4 × diameter + L.
Repeat the experiment using a tuning fork of different frequency.
Wavelength = 4 × corrected length of air column.
Velocity of sound = frequency of tuning fork × wavelength.

26.5.2 Speed of sound with tuning fork
Speed of sound with a tuning fork to resonate a pipe
| See diagram 26.5.2: Resonance tube
| See diagram 26.3.02: Reservoir-resonance tube apparatus
1. A tuning fork can make the closed air column form a standing wave.
Strike a tuning fork then hold it over the open end of a resonance tube in which the inner cylinder can be raised until resonance is
heard.
Another method is to use a measuring cylinder to be filled with water until resonance occurs.
For the frequency range 360 to 512, corresponding to a 3/4 lambda mode with the open end being the antinode.
The antinodes (A) are displacement antinodes (pressure nodes) and the nodes (N) are displacement nodes (pressure antinodes).
If the frequency is fixed, as in the case of the tuning fork held over the open end of a tube:
The resonance lengths are v/4f, 3v/4f, 5v/4f and so on for a tube closed at one end.
The resonance lengths are, and v/2f, 2v/2f, 3v/2f for a tube open at both ends.
At resonance exists, the displacement is a minimum, i.e. a node, at the bottom closed end, but the antinode is a small distance beyond
the open end, called the end correction, e.
A water reservoir-resonance tube apparatus 1m long, tuning forks frequency 500 Hz, allows three positions of resonance,
L1, L2, and L3.
So wavelength of the sound wave = 4(L1 + e), 4/3(L2 + e), 4/5(L3 + e).
So wavelength = 2(L2 - L1), 2(L3 - L2) (L3 - L1).
For a closed cylindrical tube 1 m long, inside diameter 2.80 +- 0.01 cm, tuning forks of 480 Hz (B4) and 512 Hz (C5), e = 1.28 +- 0.05 cm.
Speed of sound, v = frequency of the tuning fork × wavelength.

Experiment
2. Fix the a U-tube on the stand.
Pour water into the two glass arms.
Lift the right tube so that the surface of water in the left tube is just under point A, at the end of the left tube.
Knock the highest frequency tuning fork with a rubber hammer to start its vibration.
Put this tuning fork above the left tube.
Lower the right tube to lower the surface of water at the left tube so that the air column between the end and surface of water in the left
tube is lengthened.
When the water surface goes down from point A to C, the sound reaches the maximum.
It resonates with the tuning fork. The fundamental of the air column is the same as the frequency of vibration of the tuning fork.
Measure and record the length l1 of the air column AC here.
Lengthen the air column AC further until you hear the resonance sound of the air column.
Knock the tuning fork again to make it keep vibrating.
Find the position of the second resonance point.
Record the length l2 of the air column AC.
Record the frequency of the tuning fork and the room temperature.
Calculate the speed of sound by: v = 2f (l2 - l1).
Repeat the experiment using other tuning forks and calculate the speed of sound.
3. Calculate the average of speed of sound and record as m / s.
The point A at the open end is the antinode of the standing wave.
Point C on the water surface is analogous to a fixed end is the node.
The distance between the node and the antinode is odd number times of 1 / 4 wavelength.
l1 + e = w / 4, corresponding to the first resonance point
l2 + E = 3w / 4, corresponding to the second resonance point, where w is the wavelength of the tuning fork, E is the correction of length.
E is used to adjusted the value of the length, because there is a short distance between the tuning fork and the end of left tube.
The length of the air column is slightly larger than the length of AC, the first formula above minus the second minus may get rid of E and
get : (l2 - l1) = w / 2, so w may be found.
As v = fw, the speed of sound may be found.

26.5.3 Speed of sound with a drum
The speed of sound in air at 20oC is about 334 m / s.
The speed of light is 299, 792, 458 m / s.
1. Use a large drum, a 1 metre circumference trundle wheel or long measuring tape.
Arrange students, on a calm day, in a large open area, e.g. an oval or a quiet straight road.
Hit the drum every half second using a watch or borrow a metronome from the music department or use a 1 metre long pendulum.
Walk 50 metres away from the drummer then the drummer repeats the exercise.
Walk another 50 metres and repeat.
At about 170 metres from the drummer you can observe that the drummer is hitting the drum exactly as the sound is heard but after
stopping one "extra" beat is heard.
If you assume that the light reaching the observer travels instantaneously from the drummer, the distance travelled by sound in a half
second about 170 metres, that tells us the speed of sound is about 340 metres per second.
2. Compared with the speed of sound, the speed of light is infinity, in air sound waves travel uniformly, viz. the speed of sound is a
constant so it may be calculated applying the formula on reform motion.
Use a drum or a wasted metallic pail, a piece of tape measure, a metronome or a single pendulum.
Do this experiment at a silent and open playground.
Beat the drum 2 times every seconds, 6 times in all.
It is better to use the metronome to control the beating rhythm to assure the interval coincident and exact.
Discover the difference in time between beating the drum and hearing the drum.
When observe and hear around the drummer firstly, you may see beating drum and hear the drum at the same time, at 50 m far away
from the drummer.
Secondly, you may see beating drum before hear the drum at the same time, but the difference in time is not large, at 100 m far away
from the drummer .
Thirdly, you may see beating drum before hear the drum at the same time, and the difference in time is obvious.
Continue to see and hear.
At 170 m far away from the drummer, you do not hear the drum when you see the first beating, you hear the first drum at the same time
you see the second beating, you hear the second drum when you see the third beating, you may hear a "extra" drum at 0.5 s after the
drummer finishes his beating.
Put t = 0.5 s and s = 170 m into the formula v = s X t, then get v = 340 m, i.e. the approximation of the speed of sound.
At this experiment suppose that the speed of light is infinity, viz. the action of beating seen and the action of practical beating happens
at the same time no matter how far away from the drummer.
It will cause some error but very small.
So the speed of sound obtained with the approximate method processes is true enough.
If there are 2 cellular phones, one around the drummer, another being carried at the observer, their loudspeakers may receive the drum
at the same time, because electromagnetic waves travel at the same speed with that of light.
In a sailboat race, the contestants should all start as soon as they see the smoke from the starting gun, not wait to hear the sound of
the gun.

26.5.4 Speed of sound with echoes
1. Clap your hands 100 m from a high wall.
Keep clapping steadily until each clap coincides with the echo of the last clap.
Use a stopwatch to record the time between these claps.
Measure the distance from the wall.
During the time between claps the sound travels twice the distance from the wall.
The speed of sound in air at 0oC is about 331 m / s.
2. You need two pieces of wood to make a clapping sound, open space and a vertical flat surface outdoors, e.g. wall of school
building.
Face the wall 20 meters from the wall, and move very slowly backwards while clapping with the two pieces of wood pieces.
When an echo of the clapping sound is heard, measure the distance.
The minimum time interval that the human ear can detect between two claps is 0.1 second.
When this interval between the clap and the echo is shorter than 0.1 second, no echo is heard, so you hear no echo when you stand too
close to the wall.
By moving slowly backwards away from the wall, an echo will be heard at a certain moment.
At this moment, the echo came back within 0.1 second, the distance between observer and the wall is measured (about 17 m), and the
speed can be calculated from:
distance sound travelled (2 × 17 m 9 34 m) divided by the time (0.1 sec) equals 340 m / sec.

26.5.5 Speed of sound in solids
1. Place one ear to the desk and tap the desk top with the end of a ruler.
Note whether the sound is louder than when passing through the air.
You can place your ear to the ground to hear animals or to railway lines to listen for approaching trains.
Put your head under water while in a bath or swimming and tap the side.
Ultrasound can be used to take a picture of an unborn baby.
You can listen through a wall by placing an empty glass between the wall and your ear.
The glass acts like a stethoscope.
2. Sound waves travel faster in solid and liquid than in air.
The speed of sound is dependent on the medium.
Press your ear close to a tabletop and gently knock the tabletop with an end of a ruler or the neb of ball point pen.
You may hear the sound through the table clearer and louder than in air.
American Indians press their ears close to the ground to listen attentively to wild animals' running from afar.
If someone presses the ear close to a rail, he or she may hear the sound that train wheels bump against the rail at a distance.
Repairmen often press one end of a stick (or a ruler, a screwdriver) on the outer covering of a running machine and press the ear close
to the ruler thus they may hear any abnormal sound from the inside the machine.
These observations show that the sound waves travel better in solid than in air.

26.5.6 Speed of sound in liquids
Immerse your head into water at a basin or swimming pool.
Gently knock the wall with your hand and listen attentively to the sound.
When your head is above the water, knock the wall of the basin with the same magnitude of force.
Compare the sounds.

26.5.7 Speed of sound in liquids with bubbles
A heating element superheats water causing steam bubbles that pass out into the surrounding cooler liquid and collapse.
The collapse makes shock wave the causes the "singing" kettle.
1. Observe the sound in a liquid.
Pass bubbles through the liquid and note the pitch of the sound drops.

26.6.1 Tones
In general, musical sounds are made up of a certain limited number of frequencies.
A resultant wave includes a set of simple harmonic waves, in which the fundamental frequency, f1, is the lowest and nf1 is harmonics.
A musical note has a characteristic pitch, loudness and quality.
The pitch of a sound is related to its frequency of vibrations, the "highness" or "lowness".
The pitch is dependent on the fundamental.
The loudness of a sound depends on the ability of the ear to "hear", which depends on the movement of the eardrum as sound waves
arrive.
The bigger the movement of the ear drum, the stronger will be the signals sent to the brain, and the louder the sound you hear.
The loudness is the psychological reaction to the intensity of a sound.
Quality or timbre is another parameter related to the psychological reaction.
The quality depends on the amount of the harmonics.
A toy whistle emits tones at 2081, 1896 and 1727 Hz.
Subjective difference tones at 169, 185 and 374 Hz are clearly audible.
Two pure tones produce beats or difference tones.

26.6.6 Bottle sounds
See diagram 26.3.1.6: Bottle sounds
Blow across a set of bottles with water levels adjusted to give a scale.

26.6.7 Siren
An air jet is directed at a rotating disc with holes.
Air is blown through concentric rows of regularly spaced holes on a spinning disc.
Change of speed of the disc changes frequencies but not intervals.

26.6.8 Musical saw
A card is held against a dull saw as the sawing speed is varied.

26.6.9 Savart wheel
See diagram 26.6.9: Savart wheel
1. Show that the pitch of a musical note is dependent on the rate at which the ear receives impulses, i.e. the pitch of a note is depends
on its frequency.
Use a series of toothed wheels mounted on a common hub rotated by a pulley and motor.
Hold a card against one of the rotating wheels and hear the characteristic sound with frequency proportional to the number of teeth and
the speed of the motor.
Decrease the wheel speed by applying greater pressure against the wheel to cause proportionate decrease in the pitch of the emitted
sound.
Wheel 1, 33 teeth, Wheel 2, 34 teeth, Wheel 3, 37 teeth, Wheel 4, 38 teeth, Wheel 5, 41 teeth, Wheel 6, 44 teeth, Wheel 7, 46 teeth,
Wheel 8, 49 teeth, Wheel 9, 51 teeth, Wheel 10, 55 teeth, Wheel 11, 58 teeth, Wheel 12, 62 teeth, Wheel 13, 66 teeth.

2. A set of gears on a single shaft of a variable speed motor have the ratios of frequency and pitch.
Hold a stiff cardboard against the rim of a spinning toothed wheel.
Use wheels on the same shaft each with different numbers of teeth.
A tooth ratio scale is a set of gears with teeth are mounted coaxially on a shaft connected to a variable speed motor.
Varying the speed shows intervals are determined by frequency ratios rather than absolute pitch.

26.6.10 Attenuation and intensity with a decibel, dB, meter
Use a decibel, dB, meter to measure the intensity at various ranges.
A sound level meter is used to measure the instructor speaking.

26.6.11 Attenuation of materials
Put various materials between a sounding board and a tuning fork stuck in a block of wood.
Examine various acoustical tiles acoustical tiles

26.6.12 Reverberation time for architectural acoustics
Record toy pistol shots in various rooms then find reverberation time at different frequencies.
Clap hands to generate sound for reverberation time.
Measure reverberation time of the classroom with a dB meter.

26.6.13 Ripple tank acoustics
25.3.1.0 Ripple tank, wave tank
Put cross-section models of various auditoriums in a ripple tank to show scattering and reflection.

26.6.18 Circular glockenspiel
Play major minor augmented and diminished cords on a circular glockenspiel.

26.6.21 Microphone and oscilloscope
See: Oscilloscope (Commercial)
Examine the output of a microphone on an oscilloscope while listening to it.
Use a microphone and oscilloscope show that a tuning fork does not produce a pure sine wave but a fork on a resonance box does.

26.7.0 Reflection and refraction of sound, sound lens, reverberation, speaking tubes, whispering galleries, zones of silence, sound
ranging, echo sounding
Sound is reflected from surfaces to produce an echo.
Even in a room echoes are produced.
However, no distinct echo is heard because not just one reflection of the sound occurs.
Sound waves are reflected by hard surfaces, but may be absorbed by soft surfaces.
If the reflecting surface is within 10-15 metres of the sources of vibration the echo seems to join with the original sound, which then
sounds longer, a reverberation.
Reverberations is part of the technology of acoustics, which is used in designing concert halls.
Rock bands partly need massive amplification techniques because of the poor acoustics in the venues in which they play.
However, rock band singers may not be trained to project their voices and the audience often wants to hear it very loud indeed.

26.7.1 Reflection of sound
See diagram 26.7.1: Reflection of sound
Like other waves, the reflection of sound obeys the law of reflection that the angle of incidence is equal to the angle of reflection.
Experiment
Roll two paper tubes of length about 80 cm with a piece of hard paper.
Place a table near a wall.
Place a large sound insulation board on the table upright to the wall but not touching the wall.
At one side of the large sound insulation board place a tube against a wall forming an angle with the tube.
Near the below end of the tube place a clock on the table.
At another side of the large sound insulation board place another tube against a wall forming the same angle with the tube.
Listen to the sound of the clock through the below end of the tube.
Measure the original value of the angle between the tubes and wall.
Adjust the angle until the listener hears the loudest sound.
Measure the angle again.
Compare the angle's values.

26.7.2 Echoes in a ripple tank "theatre"
See diagram 26.4.9: Ripple tank "theatre"
Use a piece of poster board or construction paper, cut off a strip.
Bend the paper strip into a circle then put them into a flume.
Leave an entrance between the two ends of the paper strip then fix it.
Pour some water in to the flume, the water surface lower than the paper strips.
Place a pulse generator at the entrance to start the vibration of water.
The water waves reflect on the paper "wall" and finally form echo.
Draw the waveform of the echo you see on a paper.

26.7.3 Balloon as a sound lens, acoustic lens
See diagram 26.7.3: Sounds lens 1 | See diagram 26.7.3.1: Sound lens 2
1. The speed of sound travelling in gas depends on the density of the gas.
The denser the gas, the slower sound travels.
Sound travels at about 340 metres per second in air and about 270 metres per second in carbon dioxide.
So sound should be refracted towards the normal when it moves from air to carbon dioxide.
Blow up a balloon.
Hold it against a fairly loud source of sound.
Place your hands or cheek against the balloon to feel the vibrations.
You hear sounds when their waves hit and vibrate your eardrums.
2. A balloon under pressure has a higher index of acoustic refraction than the surrounding air, so it behaves as a sound lens.
Use a balloon and a microphone to listen to distant conversations.
Use a balloon and a tiny loudspeaker to project a sound beam to an individual listener.
Put some dry ice, frozen carbon dioxide, in a balloon.
Tie off the balloon and weigh it on a balance.
Watch the "weight" change as the dry ice sublimes.
When the balloon is fully inflated use it as a sound lens.
Use an incoherent source of sound, e.g. running water.
Use an oscilloscope and microphone to measure the speed of sound through the balloon filled with carbon dioxide then calculate the
index of refraction and focal length for the higher frequencies.
3. Hold an inflated balloon 10 cm from a transistor radio.
Squeeze the balloon between your two hands and note the feeling.
Turn up the volume of the radio and squeeze as before.
Note the difference in feeling.
4. Balloons filled with different gases either focus or defocus sound waves.
Fill the balloon with helium, carbon dioxide or air.
Place the balloon between a small speaker and a microphone and measure the microphones output.
Carbon dioxide focuses the sound but helium defocuses the sound, with air of course there is no difference.
5. Inflate a balloon with your mouth then tie its mouth.
Place the balloon between a watch and your ear and press close to each other.
You may hear the "tick tick" the watch emits.
There is more carbon dioxide in the gas you breathe out compared with air so the gas inside the blown-up balloon has bigger
proportion of carbon dioxide than air.
The balloon also contains water vapour breathed out.
The gas inside the balloon is denser than air outside the balloon because carbon dioxide is denser than air.
Sound travels more slowly in a denser gas so sound waves refract on the surface of the blown-up balloon to collect together, just like
a lens.
The sharper the curvature of the balloon lens the smaller its focal length.
Pull strings attached to the surface of the balloon to vary the thickness of the balloon lens.
As there are more sound signals arriving your ear your ear may hear very low sound more clearly.
6. Quiet or far away sounds are hard to hear because sound energy spreads out as it moves away from its source.
However, by using a balloon filled with carbon dioxide gas, you can focus sound waves to create a loud spot!
Put about 50 mL of crushed dry ice into a glass soft drink bottle.
Stretch the neck of a round balloon over the top of the bottle.
As the dry ice warms, carbon dioxide gas slowly fills the balloon, OR, place the bottle in warm water to speed up the filling process.
When full, remove the balloon and tie the neck to prevent carbon dioxide gas escaping.
You now have a "lens", which you can use to focus sound.
Balance the balloon on a coffee mug.
About one metre away on one side of the balloon, place a radio (or other sound source) with the volume control turned down so that it
is only just audible.
Move your ear around on the opposite side of the balloon.
At what point is the sound loudest?
What happens if the balloon is removed when your ear is at that point?
What happens to the loud point when you move the radio closer or further away from the balloon?
Carbon dioxide gas molecules slowly pass through the sides of the balloon, so fill the balloon just before using it.

26.7.4 Speed of sound depends on the density of the carrier gas, helium / oxygen mixture
This famous experiment should NOT be done in schools
A demonstrator exhales then takes a deep breath from a balloon containing a mixture of helium and oxygen to fill the lungs.
Do not inhale pure helium!
The demonstrator then speaks with a high pitch "Donald Duck" voice because of the velocity wavelength relationship with a lighter gas.
Velocity of sound at 0oC in: hydrogen 1286 m/s, helium 972 m/s, air 331 m/s, sea water 1533 m/s, water 1493 m/s.
Velocity of sound in air at 20oC: 343 m/s.

26.8.0 Interference and diffraction of sound, beats, stereophonic sound, interference of sound waves using an air column or a
stretched vibrating string
See: Diffraction (Commercial)
When a musician first blows across an opening of a tube an air stream forms that splits on the inside edge, so some air flows across the
tube and some air flows into the tube to cause a downward pull of air particles into the tube.
When all the air stream flows into the tube, a compression forms and the air stream splits again, but this time the part that flows across
the tube creates an upward push and all of the air stream flows across opening of the tube.
When the compression reached the bottom of the tube it was reflected by the bottom of the closed tube and the compression reflected
back as a rarefaction.
This first rarefaction caused reflected compression wave travelling up the tube leading to constructive interference with the next
compressions travelling down the tube.
At the top of the open tube, compressions are reflected as compressions, in phase with the next compression, providing constructive
interference.
The wave pattern is stabilizes as a standing wave.
The places constructive interference become the antinodes of the wave, while the areas of destructive interference become the nodes.
A tube vibrating with a standing wave pattern of three antinodes and three nodes is vibrating at the 5th harmonic.
A close tube can only vibrate at odd harmonics, 1st harmonic ( fundamental), the 3rd harmonic, 5th harmonic.
Sound waves show reflection, e.g. echoes, refraction, i.e. bend towards the normal when pass into media in which their speed is
slower, diffraction, e.g. you can hear people talking around the corner communicate easily by speech, even when on opposite sides of
a large tree trunk, and form interference patterns, e.g. beats.
Experiment
Use 3 sound insulation boards with the same size.
Drill a hole at the centre of each board.
Upright place the 3 boards parallel to one another.
Adjust their positions to make the 3 holes at one straight line.
Place a watch outside of the hole on the first board and press your ear close the hole on the third board.
You may hear the "tick tick" the watch emits clearly.
It shows the sound travels to the ear directly through 3 holes.
Move the middle board a bit to make the 3 holes not at a straight line.
Although the sound does not travel to your ear directly but you may hear the sound still because the sound waves may round the
obstacle to go ahead.

26.8.1 Beats, superposition of waves of different frequencies
See diagram: 26.8.4.4: Beats
Superposition of sound waves of similar frequency produces pulsation called beats that consist of booming sounds of wave
reinforcements alternating with quieter sounds of wave annulments.
The number of beats per second depends on the difference between the frequencies, e.g. two beats per second will occur with
combined frequencies of 200 Hz and 198 Hz.
Sound waves reflect, e.g. echoes, refract towards the normal in media in which their speed is slower, diffract, e.g. you can
communicate easily by speech even when on opposite sides of a large tree trunk, and form interference patterns, beats.
You hear different frequencies of vibration as differences in pitch, i.e. higher frequencies as high notes and lower frequencies as low
notes.
If two tuning forks with frequencies of 256 hertz and 254 hertz are sounded simultaneously and at a certain instant an observer
simultaneously receives a compression from each fork, the observer hears a loud sound.
One quarter of a second later the 256 hertz tuning fork has gained one half of a vibration on the 254 hertz tuning fork so the observer
simultaneously receives a compression from one tuning fork and a rarefaction from the other tuning fork.
The compressions and rarefactions annul, or partly annul, each other and the observer hears minimum sound intensity.
After another quarter second when one tuning fork has gained one vibration on the other, the observer again simultaneously receives two
compressions and the sound is again of maximum intensity.
So during the time interval in which one tuning fork gains one vibration on the other, the sound intensity passes through one cycle of
change, i.e., one beat is heard.
There will be two beats per second because the 256 hertz tuning fork makes two vibrations more than the 254 hertz tuning fork.
If two sources of sound of frequencies f1 and f2 are simultaneously emitting sound waves, then the source of higher frequency, f1, gains
one vibration on that of lower frequency (f1 - f2) times per second and an observer hears (f1 - f2) beats per second.
The number of beats per second is equal to the difference between the frequencies of the two sources.
If two notes of slightly different frequencies are sounded together they interfere and periodically produce a loud sounding large
amplitude called a beat.
Beats are used by piano tuners to tune instruments.
If two wave trains of frequencies 4 and 5 hertz are propagated so that each particle is subject to the joint action of the two waves, the
displacement at any instant of any particle will be the algebraic sum of the separate displacements due to each wave.
In the diagram, Curve 1. shows for a given particle the time displacement graph due to the wave train of frequency 5 hertz.
Curve 2. is the time displacement graph for the wave train of frequency 4 hertz.
The graphs are drawn in each case for an interval of two seconds.
At an instant represented by the point A, the displacements, AB and AC, due to the two separate waves are both to the same side of
the mean position of the particle and its resultant displacement at this instant is AD in Curve 3., equal to AB + AC.
At the instant of time represented by the point E, the displacements due to the separate waves are to opposite sides of the mean
position of the particle so the resultant displacement is EH = EF + (- EG).
Curve 3. is the resultant time displacement curve for any particle.
The resultant displacement is greatest when the displacement due to the waves assist each other.
This waxing and waning of the resultant amplitude due to the superposition of two waves of like kind but of different frequencies and is
called beats.
Experiment
For tuning octaves, with a tuning hammer on F#46, side strings muted with rubber wedges, strike simultaneously already tuned F#34
and F#46.
Tune by adjusting the tension in the strings until all audible beats are eliminated and the two notes sound as a single one note.
Tune G47 in the same way and keep tuning every note towards the upper end of the keyboard, then tune the bass section.

26.8.2 Interference of sound waves with tuning forks
Two sound waves of the same frequency and amplitude may give rise to easily observed interference effects at a point through which
they both pass.
If the crests of one wave fall on the crests of the other, the two waves are said to be in-phase.
In that case, they reinforce each other and give rise to a high intensity at that point.
However, if the crests of one wave fall on the troughs of the other, the two waves will exactly cancel each other.
No sound will then be heard at the point.
The two waves are then 180o, or a half wavelength, out-of-phase.
Intermediate effects are observed if the two waves are neither in phase nor 180o out-of-phase, but have a fixed phase relationship
somewhere in between.
At the certain condition, two or more sound waves interact and combine to produce a resultant wave of larger or smaller amplitude.
Experiment
Hold the handle of a tuning fork and knock it with a rubber hammer to start its vibration.
Touch the rim of a table with the top of the tuning fork.
Place the tuning fork upright near your ear.
Gently rotate the tuning fork around a vertical axis for a circle (360o).
Take care of the change in volume.
The vibration of the tuning fork generates the vibration of the table at the same frequency.
They meet the condition of interference and form the interference field.
Rotate the tuning fork to change the distribution of sound intensity.
So you may hear the loudest sound 4 times and the lowest (nearly silent) sound 4 times.
Silent zones can sometimes occur near a sound source, even when a sound can be heard further away.
This happens when sound waves speed up and are refracted as they pass through warm air.
The sound is deflected up and over a location causing a silent zone.
If the sound then hits a belt of cold air as it rises then it will be refracted down again as it slows down.

26.8.3 Superposition of waves of equal frequencies with tuning forks
See diagram: 26.8.4.1: Superposition with tuning forks
Hold a vibrating tuning fork near your ear and slowly rotate it about its shaft.
Hear the sound alternating between loud and soft.
Note the four positions in one revolution at which almost no sound is heard, about 5 dB lower.
See in the diagram the ends, A and B, of the prongs as viewed from above.
1. As the prongs approach each other, a compression forms at C and spreads out in the directions shown by the arrows from C.
At the same time the rarefaction formed at R1 and R2 spread out as shown by the arrows from R1 and R2.
So in the regions of the dotted lines a compression and a rarefaction arrive simultaneously and annul each other along these lines.
2. As the prongs move apart, a rarefaction forms at C and compressions form at R1 and R2.
The rarefactions and compressions spread out to annul each other along the dotted lines.
3. So along the dotted lines the pressure re mains constant and these lines are lines of zero sound.
The four positions of silence in one revolution of the fork correspond to the four dotted lines.
The modifications of intensity obtained by superposing waves are called interference effects.
4. However, if you sound the tuning fork at arm's length from your ear and rotate it about its long axis you will only hear two maxima and
two minima.
These two situations are called "near-field" (close to your ear), and "far-field" (arm's length) sounds.
5. Some people have reported that the minima are not symmetrically spaced at 45o from the plane of the fork, instead the first minima
occurs at approximately 54o.
6. Connect a microphone or a loudspeaker to examine these patterns on an oscilloscope.
Clamp the tuning fork to the bench and moving the loudspeaker around.
This will be no easy task.

26.8.4 Superposition of waves of equal frequencies with loudspeakers
See diagram: 26.8.4.2: Superposition with loudspeakers
Mount two loudspeakers, A and B, near each other and operate them from the same source of high frequency, e.g. 3 000 cycles per
second.
The sound waves originating at each loudspeaker are superimposed in the region in front of them.
At those points at which a compression from one loudspeaker arrives at the same instant as a rarefaction from the other loudspeaker,
annulment occurs and the sound intensity is zero.
At points where two compressions, or two rarefactions, arrive simultaneously, reinforcement results from the superposition of the two
wave trains and these points are regions of maximum sound intensity.
The thick and thin arcs represent the instantaneous positions of the zones of compression and rarefaction from A and B.
At points marked x, annulment occurs and these points of zero sound intensity lie along lines radiating from between A and B.
The points of intersection of two thick lines or of two thin ones are regions of maximum intensity.
The existence of the above pattern in the region in front of A and B can be made evident by exploring the sound field with a microphone.
It is found that alternating zones of maximum and zero sound as the microphone is moved across the sound field.
Use a sensitive flame to explore the interference pattern by keeping the flame in a fixed position and slowly rotate the sources of sound.
The flame alternately dips and rises as the lines of maximum and zero intensity pass over it.

26.8.5 Wave interference in water, drop stones in water
Simultaneously drop two identical stones or marbles or golf balls into a calm pool of water.
An interference pattern similar to the above occurs on the surface of the water.
The ripples move out in circles.
Where they cross each other note the brief patterns of constructive interference, two peaks at the same place at the same time (higher
ripples) and destructive interference, a peak and a trough meet at the same time (lower ripples).

26.8.6 Loaded tuning fork
See diagram 26.8.6: Loaded tuning fork
Use two tuning forks with the same frequency.
Wrap a piece of sticking plaster around one prong of one tuning fork.
Sound each tuning for separately.
Note that the loaded tuning fork has reduced frequency.
Sound the two tuning forks together.
Note the throbbing sound due to the waxing and waning of the resultant amplitude.

26.8.7 Resonating objects have same frequency as source of vibration
Put two upright stands 50 cm apart and attach a string between them at the same height.
Tie the short lengths of string to seven metal washers.
Hang the washers on the horizontal string at the following hanging string lengths:
washer l (20 cm), washer 2 (15 cm), washer 3 (20 cm)., washer 4 (15 cm), washer 5 (5 cm), washer 6 (10 cm, washer 7 (5 cm).
Start swinging washer 7 and observe the other washers.
Washer 2 and washer 4 starts swinging with swing with washer 7.
Repeat the experiment with washer 2 swinging first.
Repeat the experiment with washer 1 swinging first.
Washer 3 starts swinging with it.
Washer 7 can be compared with the source of vibration and washer 2 and washer 4 have the same frequency of vibration.
The same happens when washer 2 or washer 4 is started to swing first.
The washers that have the same hanging string length will swing with the original swinging.
The source of vibration can increase its own vibrations, e.g. when wind blows on it.

26.8.8 Interference of two sound sources
See diagram 26.8.8: Two speakers interference diagram
Feed a signal from a signal generator into the auxiliary input of a stereo amplifier and set to 3-5 kHz.
Position the speakers about 2 m six feet apart, directed towards the audience.
Move the microphone probe along line A-B to see the nodes and antinodes displayed as minima and maxima on the C.R.O.

26.8.9 Ultrasonics, ultrasonic interference
Ultrasonics are vibrations whose frequencies are higher than the upper audibility limit for humans, i.e. 20 kHz.
Sound waves show reflection, e.g. echoes, and refraction, bend towards the normal when pass into media in which their speed is
slower, e.g. you can hear people talking around the corner or on opposite sides of a large tree trunk.
Ultrasonic waves are used by bats for navigation in the dark, and used by ships in the ultrasonic system called sonar to find fish and
measure the depth of the sea.
For jet planes the speed of sound is measured in Mach numbers (Ernst Mach 1838-1916).
A Mach number is the ratio of the velocity of an object in air to the velocity of sound in air.
Sonic speed = the speed of sound.
Subsonic speed < speed of sound.
A jet plane travelling at supersonic speed, i.e. > Mach 1, is travelling faster than the speed of sound and leaves a cone shaped shock
wave behind it heard as a very loud noise called a sonic boom.
A jet plane "breaks the sound barrier" when its speed increases through Mach 1.
The sound barrier divides subsonic speed from supersonic speed.
The first pilot to "break" the sound barrier and survive was Captain Chuck Yeager in 1947 working in an US government program.
Experiment
Ultrasonic interference
See diagram 26.8.9: Ultrasonic interference diagram
Connect two ultrasonic transducers to a signal generator set to their resonant frequency of 26 kHz.
Connect a third transducer to a C.R.O. and placed at right angles to the line joining the transmitters.
Move the receiver is moved along this line to display maxima and minima on the C.R.O.

26.8.9.1 Two slit interference with microwaves
See diagram 26.8.9.1: Two slit interference diagram
Direct a microwave transmitter towards a large metal screen with two slits separated by a distance comparable to the wavelength, 3 cm.
Move the receiver along the line AB, to observe maxima and minima depending on the path difference of the waves from the two slits.

26.9.0 Analogue and digital recording
The three types of recording mechanisms are mechanical, magnetic and optical.
In analogue transmission the characteristic of the transmission signal, e.g. amplitude or frequency, varies in direct proportion to the
received sound or brightness of a picture.
The hands of a clock is a form of analogue recording.
In digital transmission the information is transmitted in a series of pulses thus eliminating unwanted noise.
The pressure from a sound wave can be sampled many times in a second and the values recorded in numerical form using the binary
code.
The closer the sampling the higher the fidelity of the sound recorded, i.e. more closely repeats the original sound.
Later this information can be translated into the analogue form in the receiver.
Digitally recorded information can be stored on a CD or sent through the internet.
Analogue and digital units
An analog signal is a continuous signal which represents physical measurements.
Analog instruments usually have a scale which is cramped at lower end and give considerable observational errors.
Digital signals are discrete time signals best suited for computing and digital electronics.
Digital instruments are free from observational errors like parallax and approximation errors.
Whether digital is more accurate than analogue depends on the application.
A digital meter requires you to convert and compare present to a desired value by maths.
Analogue meters relay a positional comparison that can be done in a glance.
In motor vehicles the speedometer is usually analogue because it is easy to read and accuracy as it can be a distraction.
Most driver glance at the speedometer to check whether the vehicle is within the legal speed limit, but it is also an indication of safety in
certain road situations.
The accuracy of a speedometer to measure ground velocity can be affected by the tyres used and their pressure.
The speed of a motor vehicle has usually constantly varying values, which are much easier to see and recognize patterns with analogue
meters than digital meters.

26.9.01 Telephone carbon microphone, transducer, load cell
1. A carbon microphone in a telephone has an aluminium diaphragm outside two carbon blocks in a mixture of carbon granules.
The carton blocks connect to a power source and a receiver.
Sound waves cause the diaphragm to vibrate that in turn causes the carbon blocks to move together or apart and change the current
between the power source and the receiver.
2. In the receiver, the variable current from the microphone passes through the coils of an electromagnet that exerts variable magnetic
force on an iron diaphragm to produce sound waves.
3. A transducer converts a physical quantity, e.g. volume of sound, brightness of light, temperature of hot object, into an electric signal,
or converts an electric signal into a physical quantity.
Transducers usually convert a non-electrical signal into an electrical signal.
Transducers are used in microphones and loudspeakers (electroacoustic transducers), photocells and accelerometers.
A recording head may consist of a magnetic, electric, mechanical or electro-optical transducer to record sound on magnetic tape,
compact disc or film.
A passive transducer has only the incoming signal as its power source but and active transducer has an additional external power source
for power gain.
4. A load cell, e.g. OMEGA's DLC101 dynamic load cell, can measure force transients or dynamic force pulsations in impact or
vibration applications.
It contains a thin piezoelectric crystal that generates an analog voltage signal in response to an applied dynamic
force.
It has 2 threaded ends to allow installation of threaded members, e.g. mounting studs, impact caps, and machine elements.
Its welded construction encloses and protects the crystals from the environment.
Experiments
Dismantle old telephones and locate the carbon microphones.

26.9.2 Microphone and loudspeaker
See: Electrical equipment, Loudspeaker, (Commercial)
See diagram 26.9.2: Moving coil loudspeaker
Microphones contain a transducer to change one form of energy into another.
This is actuated by sound waves.
The microphone delivers electric signals proportional to the sound pressure.
Sound hits a diaphragm made of paper or plastic and vibrates it.
The vibrations are then converted into electric current.
Experiments
1. Wind the thick insulated copper wire around the dowel to make a coil 3 cm in diameter.
Then wire up a circuit consisting of the battery, the rheostat and the copper coil.
Glue a refrigerator magnet onto the cloth then hang it at one opening of the coil.
Complete the circuit.
Note how the magnet moves in response to the changing magnetic field that is produced in the coil as you change the setting on the
rheostat.
A loudspeaker works in exactly the same way as a microphone, but in reverse.
An electric current from a microphone flows through the coil in the electromagnet that has a central pole and a surrounding ring pole.
The force between the magnetic field of the coil and the magnet makes the coil vibrate in accordance with Fleming's left hand rule and
the attached paper cone diaphragm vibrate to create sound waves as it pushes and pulls on the air next to it.
2. Make some recordings of different people speaking.
Recite a few ditties such as she sells seashells on the sea shore and Peter Piper picked a peck of pickled peppers.
Play them back and listen to the quality of the sound.
Listen for whistling and sound of breathing.
Now try some different locations.
Make a recording outside, make one in a hard reflecting room and one in a soft absorbing room.
Find a windy place and make another recording.
Again listen to the recorded sound.
Watch a few interviews on television and take note of the different styles and types of microphones in use, e.g. "fluffy dogs" (large fluffy
microphones used outside) and lapel "mikes" (microphones).
Try to improve sound quality in your recordings.
Recite at different distances from the microphone.
Try drinking some water to stop sound of breathing and hissing sounds.
Experiment by wrapping different types of cloth or sponge around the microphone to cut out other unwanted sounds.
3. Find direction of sound with a microphone.
Some microphones are directional and pick up sounds only coming from one direction.
Set up a microphone and speakers in a room.
Position the microphone at the front of the room with the speakers as far away from it as possible.
Watch someone speaking into the microphone.
Does the sound appear to be coming from this person or the speakers at the other end of the room?
Next time you are watching a film at the cinema, try to find where the sound is coming from.
Not all the speakers are located at the screen.
Does the speech appear to originate from the people on screen or from the speakers located around the theatre?
See if you can find where the speakers are and which sounds (speech or music) are emanating from which speakers.
Listen to a stereophonic or quadraphonic sound system to experience surround sound.
Next time you are in a noisy car try to find where the sounds come from.

26.9.3 Cassette recorder
1. A cassette recorder consists of the protective plastic holder, the cassette, and two reels to allow the magnetic tape to pass from one
reel to the other through an electromagnet recording head / reading head.
Rewinding allows repeated use.
Sound is recorded on the tape with magnetized particles of iron or chromium oxide.
Electric current from a microphone that varies with a sound wave passes through a metal coil in the recording head that causes changes
in its magnetic field to rearrange the random pattern of the metal particles on the "blank" magnetic tape into a pattern that can be read by
the playback head as a sound wave to be amplified by a loudspeaker.
Experiment
Select a cassette container containing songs that you do not like.
Unravel part of the magnetic tape from the recorder and pass a strong magnet over it.
Play the cassette and the songs you do not like sound worse.

26.9.4 Compact disc, CD
A compact disc, CD, stores sound as a binary code, represented by tiny pits or bumps etched into a layer of aluminium surrounded by
flat areas called "land".
This is then coated with plastic for protection.
When the laser beam is shone at the disc some of it is reflected back by the smooth aluminium land but not by the pits or bumps.
Light reflected from the shiny underside land is read as binary 1.
Light that hits the pit or bump is scattered and not reflected, so it is read as binary 0.
The result is a series of digital pulses to be converted to sound by a loudspeaker.
The laser itself does not touch the disc so it should not wear out.
When the laser is tracking the speed of needle as it goes from the outside disc near the centre the disc spins at 500 revolutions per
minute, towards the centre of the record.
When it is tracking near the edge it spins at only 200 rpm so the same relative speed is maintained.
The "bumps" on the smooth surface of compact discs, CDs, cause destructive interference of laser beams reflecting from the sides of the
bumps, but no interference reflecting from the tops of the bumps or between the bumps.
Experiment
Let white light fall on the underside of a compact disc and note the diffraction caused by light passing through the gaps between the
bumps.

29.9.6 Gramophone record, "vinyl"
A gramophone (US phonograph) reproduces sound using with a stylus or needle that vibrates by following a groove on a revolving
spiral disc made of vinyl plastic
The needle vibrates in the groove and vibrates a diaphragm.
The sound produced this way is then made louder (amplified) by the horn on an old gramophone.
The original stylus was like a thorn and could be kept sharp with a pencil sharpener.
With repeated use the groove became worn causing loss of accuracy of the recorded sound and new sounds caused by dirt and dust.
This is a mechanical recording method.
Experiments
1. Poke a pin through the centre of the base of a polystyrene or cardboard cup.
Set the record on a turntable and start the turntable spinning.
Carefully hold the pin in the groove on the record and listen to the record at the opening of the cup.
The sound recorded in the grooves is being picked up by the pin and then turned into vibrations and transmitted by the cup.
Try the same activity with different sized cups.
How does the size of the cup affect the sound produced?
2. Cut a point on one end of a match stick.
Cut the other end into two, length wise for about 1 / 4 the length if the match stick.
Fit a piece of stiff paper into the split end.
Hold the matchstick and paper point down onto an old 78 rpm phonograph records turning on a turntable.
You can hear music coming from the paper.
When you hold the match point in the grooves of the phonograph records the lateral vibrations from the grooves are transmitted to the
paper.
Vibration of the paper produces vibrations in the air that carry to your ear drum, so you hear the sound.

26.9.7 Glass tube with an open end, using signal generator
1. Connect the loudspeaker to the fan out [viz.
outlet] of the signal generator with a piece of leader and place the loudspeaker at the open end of the glass tube.
Turn on the signal generator and adjust it to the lowest frequency.
The lower the frequency, the lower it sounds.
Gradually increase its frequency slowly until the sound increases suddenly, here the air inside the tube resonates with the sound of the
signal generator so that a standing wave forms at the lowest frequency inside the tube.
The lowest frequency is called the fundamental, denoted as f1.
Measure the length of the glass tube, denoted as L.
f1 may be expressed as, v = f1w1, where v is the velocity of travelling wave along the air column, i.e. the sound spreading velocity in the
air, w1 is wavelength, w1= 4L.
Gradually increase its frequency slowly again until the sound increases suddenly secondly.
It shows that the air inside the tube and the frequency of forced vibration meet the condition of resonance again.
The second standing wave forms, called harmonic wave, its wavelength, i.e. harmonic length denoted as L1 and its frequency
denoted as f2.
List the top four resonance frequencies.
The sound velocity is a constant under that temperature and the glass tube has only one open end.
So the frequency of the standing wave of the air column inside the glass tube is limited.
At the closed end of the glass tube, the air molecules do not move, so here must be the node of the standing wave.
At the open end, the air pressure is always equal to the atmosphere pressure so here the air is not contracted, i.e. it has no change in
shape.
So the open end must be the antinode of the standing wave.
When the air column emits the first standing wave, there are only one node and one antinode in the tube according to the vibration of the
fundamental.
When the air column emits the second standing wave, there are two nodes and two antinodes and the frequency of vibration is as
three times as the fundamental.
The vibration of the air column inside the tube with only 1 open end may just form the standing wave whose frequency is odd number
times of the fundamental.
2. Glass tube with two open ends, using signal generator
Methods are the same as above.
The 2 ends of the glass tube are all open so the two ends are all the antinodes of the standing wave.
Corresponding to the vibration of the fundamental, there are one node and two antinodes in the tube, then two notes and three antinodes
corresponding to the vibration of two times of the fundamental.
Thus the vibration of the air column inside the tube with only two open ends may form the standing wave whose frequency is even
number
26.9.8 Sound waves extinguish a fire
Fire can be extinguished by amplified tone because pressure waves sound disrupt the air enough to snuff out the flame.
Similarly oil well fire fighters use explosives to put out flames when the blast wave pushes away the oxygen that fuels the fire.
A Defense Advanced Research Projects Agency (Darpa) has developed a fire extinguisher for use in small spaces using two speakers
playing a specific low frequency either side of a liquid fuel flame.
The sound increases air velocity to thin the area of the flame where combustion occurs, i.e. the flame boundary, making the flame is
easier to extinguish.
The acoustics also disturb the surface of fuel and create higher fuel vaporization that widens the flame, making it less concentrated and
easier to extinguish.