School Science Lessons
(UNPh26)
2024-09-16
Sound
Contents
26.1.0 Pitch, frequency
26.2.0 Resonance in air columns, musical instruments
26.3.0 Resonance in strings, musical instruments
26.4.0 Sound
26.5.0 Tuning forks
26.6.0 Ultrasound
26.1.0 Pitch, frequency
26.1.01 Pitch, frequency, intensity, power of sound, concert pitch
26.1.1 Hanging buckets, change in pitch
26.1.2 Pitch and length,
26.1.3 Pitch and tension
26.1.4 Record player, change in pitch
26.1.5 Stretched rubber band, change in pitch
26.1.6 Thin and thick strings, change in pitch
26.1.7 Whirling pipes, pitch and length
26.2.0 Resonance in air columns, musical instruments
26.2.01 Resonance in air columns
26.2.1 Blow over open and closed drinking straw
26.2.2 Bottle xylophone
26.2.3 Bunsen burner and trombone resonance
26.2.4 Drinking straw oboe and trombone
26.2.5 Glass harmonica
26.2.6 Humming paper tube
26.2.7 Reed vibrations
26.2.8 Resonance in aluminium pipe
26.2.9 Resonance in paper pipe or drinking straw
26.2.10 Slide whistle, piston flute
26.2.11 Wind instruments resonance
26.3.0 Resonance in strings, musical instruments
26.3.01 Sonometer, monochord, Mersenne's law
26.3.1 Paper rider method, fundamental of string
26.3.2 Piano string resonance
26.3.3 Pitch and mass (density) of vibrating strings
26.3.4 Plastic bottle guitar, stringed instrument
26.5.13 String resonates with tuning fork
26.3.6 String vibrates at constant length
26.3.7 String vibrates at constant tension
26.3.8 Violin strings and piano strings
26.4.0 Sound
Sound
26.4.1 Cellophane noise
26.4.2 Comb resonator, amplify sound from comb, chimes
12.4.4 Decibels dB, Sound pressure units (Pa)
26.4.3 Drink-can to amplify the sound of a thread
12.6.0 Hearing
26.4.4 Insect footsteps in a paper bag
26.4.5 Knocking on bottles, blowing over bottles
26.4.5a Knocking sounds
12.4.1 Loudness, threshold of hearing, audible limits
26.4.6 Materials that absorb sound
26.3.2.3 Musical scales, tones, sharps and flats, equal temperament scale
26.3.2.9 Musical instruments
26.1.0 Pitch, frequency
26.2.0 Resonance in air columns, musical instruments
26.3.0 Resonance in strings, musical instruments
26.4.7 Sea wave patterns and sound wave patterns
26.4.8 Seeing and feeling vibrations that make sound waves
26.4.9 Sound cannot travel through a vacuum
26.4.01 Sound, sound waves, reflection, refraction, diffraction
18.0 Sound (Primary)
12.4.2 Sound pressure level
37.1.6 Speed of sound, Thunderstorm (See 3.)
26.4.10 Sound waves travel through wood
12.4.9 Stationary waves in Chinese temple "fish wash" dishes
26.4.11 Tap different containers
12.4.3 Threshold of hearing
26.4.12 Timbre and pitch
26.5.0 Tuning forks
26.6.0 Ultrasound
9.102 Voice and speaking
12.4.7 Wine glass resonance
12.4.8 Wine glass breaks with voice resonance
26.5.0 Tuning forks
26.5.01 Tuning forks
26.5.1 Beats with two tuning forks
26.5.2 Beats from heated tuning forks
26.5.3 Forced vibration from tuning forks
26.5.4 Frequency of a tuning forks with a sonometer
26.5.5 Reflections from tuning forks
26.5.6 Tests for materials that absorb sound with tuning forks
26.5.6a Tuning forks make a pure note when struck and allowed to vibrate.
26.5.7 Tuning forks move ping-pong balls
26.5.8 Tuning forks in strobe light
26.5.9 Tuning forks with oscilloscope
26.5.10 Tuning forks with same frequency
26.5.11 Sound wave patterns of tuning forks, waveform of tuning forks
26.5.12 Speed of sound in air and frequency of tuning forks
26.5.13 String resonates with tuning fork
26.5.14 Wave patterns of a tuning fork
Experiments
26.5.15 Feel vibrations with a balloon
26.5.16 Oscillation of object and production of sound
26.5.17 Sound wave patterns, oscillations, origin of sound, tuning fork vibration
26.5.18 Vibrating desk, blackboard, chalkboard
26.5.19 Vibrating cereal grains
26.5.20 Vibrating drums and balloons, ping-pong ball and tuning fork
26.5.21 Vibrating ruler
26.5.22 Vibrating speaker
26.5.23 Vibrating tuning fork touching water
26.5.24 Vibrations in bowls
26.5.25 Vibrations in wind harps, Aeolian harp
26.5.26 Vibrations of soap film
26.1.01 Pitch, frequency, intensity, power of sound, concert pitch
1. Frequency
Frequency describes how fast something is vibrating.
one Hertz is one vibration per second.
The SI derived unit for frequency is the hertz, Hz, one cycle per second.
1 kilohertz, kHz = 1000 hertz, Hz.
Frequency is the primary stimulus for pitch although many people hear a small pitch change when the intensity of a constant frequency sound is changed.
Frequency of a vibrating string is inversely proportional to its length.
The frequency will be doubled for a string that is only half as long.
Frequency is increased by increase in tension.
Four times the tension in the string will double the frequency at which it vibrates.
Frequency varies inversely as the square root of the string's density.
When you increase the density of the string, you will slow down the vibration rate and decrease the frequency.
2. Pitch of a note
The pitch of a sound is how "high" or "low" it sounds.
As frequency of the vibration of particles increases, the pitch of a note is raised.
Pitch is affected by the mass, the length and the tension of the vibrating medium.
Pitch refers to when you hear different frequencies of vibration that are called differences in pitch,
i.e. higher frequencies as "high" notes and lower frequencies as "low" notes.
When you think of a sound (say, a musical note) as either "high" or "low", you are referring to its pitch.
The higher, the higher the pitch of the sound.
When you think of a musical note as either "high" or "low", you are referring to its pitch.
The higher the note, the higher the pitch of the sound.
The sounds you hear are the result of perceiving by your ear the oscillations of an elastic medium, usually air.
Sound can be described both in terms of its physical nature and your psychological reaction to it.
As a physical wave, a sinusoidal sound wave has a frequency.
Your psychological reaction most closely related to frequency is pitch, i.e. the highness or lowness, or "bass" or "treble" of your reaction.
The range of frequencies to which your ears are sensitive is about 20 Hz to 15 000 Hz.
The human ear is most sensitive to frequencies in the 3.0 to 3.5 kHz range.
The ear canal, treated as a closed column with length 2.5 cm, has a resonance frequency equal to 3.3 kHz.
3. Intensity
Intensity is a physical parameter associated with sound related to the sound energy crossing a region in space per unit area per unit time.
The intensity, I, of a wave is the energy per unit area, per unit time.
In practice, it is the average power carried by the wave through a unit area perpendicular to the direction of propagation of the wave.
If at time dt an amount of energy dE is carried through an area dA perpendicular to the propagation direction of the wave.
Then I = dE / dA × dt = Power per unit area, W /m2.
4. Power
The power of sound is very low.
An orchestra of 75 persons playing at its loudest only produces about 70 watts of acoustic sound power.
The human car can detect tones with a power output of a millionth of a watt per square metre of area in those frequencies to which it is most sensitive.
Snow absorbs most of the sound energy that hits it.
However, it makes no difference how loud or long you shout at it, you will still not produce enough energy to melt the snow.
A crowd of 80 000 people at a football stadium makes a lot of noise, but they do not generate enough energy over a 90 minute match to cook an egg.
As sound waves move away from their source their intensity decreases rapidly according to the inverse square law.
Sound travels further over water.
This may happen if there is a warm layer of air over the water.
When the sound hits this layer it will travel faster and therefore further.
5. Concert pitch
Concert pitch is the degree of sharpness of flatness used by a group of musicians playing in concert.
The most common value of concert pitch is that the A above middle C should be tuned to 440 Hz, but higher concert pitches are becoming popular.
Before a concert starts, the separate members of the orchestra tune their instruments to a note given out by the principal oboe.
However, this could be done by using a well-tuned piano.
The oboe is used, because its pitch is exact and its penetrating sound makes it easily audible over all the other instruments in the orchestra.
The interval between two musical notes that have fundamental frequencies in ratio 2: 1.
Pitch refers to the sound you hear being high, high frequency, or low, low frequency.
Pitch is not quite the same a frequency, because at very high or very low frequencies the loudness affects pitch of the sound you hear.
26.1.02 Sol-fa
An octave may be sung using the tonic (keynote) sol-fa (solfege) syllables: doh, ray, me, fah, sol, lah, te, doh.
Each tone is given a name according to its relationship with other tones in the key.
This scale was invented by the Rev John Curwen, England, 1816-1869.
Experiments
1. Attend a symphony concert.
Observe the oboist giving a tuning not to the whole orchestra.
2. Play a cassette and place your hand against the speakers.
Turn up the volume to feel the vibrations as you turn up the volume.
Feel the vibrations of high fidelity speakers for a high note and a low note.
3. Put a small V-shaped piece of paper on a stretched string or the string of a musical instrument.
Pluck the string and note the motion of the paper.
26.1.1 Hanging buckets, change in pitch
See diagram 26.2.8: Hanging buckets.
Use separate strings with different lengths to hang identical buckets full of sand.
Strike each string and note the pitch.
Note that strings under the same tension, the pitch are depends on the length.
The longer the string, the lower the pitch.
Players of stringed instruments apply this principle to change the length of the string to control the pitch of a musical instrument.
26.1.2 Pitch and length
See diagram 26.2.1: Pencils between string and meter stick.
See diagram 26.2.1.2: Finger on string.
1. Tie a loop of string to just fit tightly around the length of a metre stick.
Insert two pencils between the string and the metre stick at each end.
Insert two pencils at each end between the string and the metre stick.
Pluck the string in the centre and note the pitch and loudness.
Put the metre stick on the desk to amplify the sound.
2. With one finger push the string down on the metre stick at the centre and use another finger to pluck gently the string on one side.
Note how the pitch and loudness changes.
Move your finger to different positions along the metre stick and pluck on either side.
Note how changing the length of the plucked string changes the pitch.
3. Tie a loop of string to just fit tightly around the length of a metre stick.
Insert two pencils between the string and the metre stick at each end.
Adjust the tightness of the string by pushing a ball point pen cap between one end of the string and the metre stick.
Place the metre stick flat on a table.
Pluck the middle of the string.
Note the pitch and loudness.
Move the ball point pen cap to different positions to lengthen or shorten the length of string that can be plucked.
Note the relationship between length of string plucked and pitch.
Compare the pitches of the two sides of the string and observe the relationship of the pitches to the lengths of two sides of the string.
4. A similar experiment uses an empty box or container with one small side cut out and a rubber band stretched around.
26.1.3 Pitch and tension
See diagram 26.2.1: Pencils between string and meter stick.
Use a ruler, fine string or fishing line, 2 ball point pens, tape.
Take the ball point pen inner out of one ball point pen.
Tape the ball point pens to each end of the ruler.
Tie the string lengthways around the ruler.
Twist the ball point pen inner around the string on the under side of the ruler.
Make sure you use the empty end of the ball point pen inner.
Tighten the string by turning the ball point pen inner through half a turn, and plucking the string each time.
Stand the ruler on the desk.
Note how increasing the tension on the string changes the pitch.
This can be shown on a guitar and other stringed instruments.
A similar experiment uses a bucket half full of sand suspended by string.
Keep adding sand and plucking the string.
Listen to the change in pitch.
26.1.4 Record player, change in pitch
Use a record player with variable speed, 33 revolutions per minute (33 rpm), 45 rpm, 78 rpm.
If the 45 rpm record is played at 78 rpm, the pitch is too high.
If played at 33 rpm the pitch is too low.
26.1.5 Stretched rubber band, change in pitch
See diagram 26.194: Stretched rubber band.
Experiments
1. Make string sounds.
Hold a thick rubber band slightly stretched between your thumb and second finger.
Pluck it with the first finger of your other hand while holding it near your ear.
Note the pitch of the sound.
Keep plucking it while stretching it more.
You expect the pitch to become higher as you stretch the rubber band, but it may seem to have the same pitch while you stretch it or even a lower pitch!
When you tighten the string of a sonometer or a violin the string emits a higher note, because the tension in the string has increased.
Also, the length and density of the string has hardly changed.
When you tighten an elastic band over your finger and thumb the tension, length and density change enough for their effects to compensate each other.
2. Stretch three identical rubber bands over an empty match box.
Increase the tension of two of the rubber bands with matchsticks between the rubber bands and the side of the match box.
Note that the pitch does increase with tension.
The lengths of the rubber bands stretched over the ends of the empty match box have much the same density and length, but different tensions.
26.1.6 Thin and thick strings, change in pitch
See diagram 26.2.9: Thin and thick strings.
Repeat experiment 26.2.1, but with two strings, one thick and one thin.
To make the tensions as equal as possible add a spacer on the underneath for the slacker string or hang a bucket of sand of the same mass from each string.
Note how increasing mass of the band change the pitch.
26.1.7 Whirling pipes, pitch and length
Use 1 to 2 metre length of articulated vacuum cleaner hose or swimming pool or bilge drain hose and string.
Attach a string to one end, hold the pipe in one hand and twirl it rapidly around.
Note how the pitch changes when you twirl it faster or slower.
Note how different length pipes affect the pitch.
Note how the air flows down the tube when you twirl it.
Australian aboriginal people have such an instrument that Europeans call a "bull roarer".
26.2.01 Resonance in air columns
Resonance Kundt's tube, (Commercial).
See diagram 26.1.1: Sound wave travelling through air.
See diagram 26.3.0: Standing waves in a string.
See diagram 26.3.01: Standing waves in air columns.
See diagram 26.3.02: Reservoir-resonance tube apparatus.
A sound wave can travel down the tube, reflect at one end and come back.
It can then reflect at the other end and start over again.
The round trip constitutes one cycle of the vibration.
The longer the tube, the longer the time taken for the round trip, and so the lower the frequency.
The harmonic series
The frequencies of these sounds are whole number multiples of the frequency of the lowest (f1).
We call them the harmonic series.
Resonance is the rapid and uncontrolled increase in the size of a vibration when the vibrating object is subject to a force varying its natural frequency.
An object that can vibrate has a natural frequency at which it will do so.
An object may be forced to vibrate at a variety of frequencies.
As recorded in the Bible, Joshua built the Walls of Jericho for protection from his enemies.
They were solidly built, but they did not do him any good when they came tumbling down at the blast from a troop of trumpeters.
What do trumpets and the Walls of Jericho, opera singers and glasses, and soldiers marching on bridges have in common?
All bodies vibrate at their normal frequency.
Resonance occurs when the frequency of a sound source coincides with the natural frequency of the body.
A string will resonate only if a whole number of segments, each a wavelength long, exactly fit on the string.
Length of resonating string = n ( wavelength) where n is any integer.
The fixed ends of the string must be nodes.
The wavelength = vT = v / f.
During resonance, the shorter the segments the higher the resonance frequency.
Longitudinal waves, compression waves occur as length wise vibrations of air columns, liquid volumes and solid bars.
At resonance, nodes exist at fixed points, such as the closed end of an air column in a tube, or the location of a clamp.
A diagram such as 26.3.0 can be used to show the resonance of longitudinal waves as well as transverse waves.
The diagrams specifically for longitudinal waves are used just to indicate the locations of nodes and antinodes.
The distance between node and adjacent antinode is 1/ 4 wavelength.
26.2.1 Blow over open and closed drinking straw
See diagram 26.3.2.14: Blow over drinking straw.
Experiment
1. Hold a piece of drinking straw against your lower lip and blow across the open end with your lips close together.
Note the tone of the sound produced by the open drinking straw.
Close the end of the drinking straw with your finger and blow again.
The tone from the drinking straw when the end is closed is about an octave lower than when the end is open.
Repeat the experiment with a shorter drinking straw.
When vibrating air changes the tone by an octave the air is vibrating twice as fast as before.
So the air was vibrating twice as fast in the open straw as in the closed straw.
The shorter the column of air the higher the sound, because air vibrates faster in a short column than in a long column.
So the pipes of an organ, e.g. a church organ or town hall organ are different sizes and lengths.
The highest sounds come from very small pipes and the lowest sounds come from very large pipes.
26.2.2 Bottle xylophone
See diagram: 26.3.1.6 Bottle sounds.
xylophone (Greek xylos wood)
Set up the bottles in a row.
Partially fill each with water.
Make sure there is a different amount of water in each.
Now tap each bottle in turn and listen to the different pitch of each bottle.
Arrange them in order from highest to lowest pitch.
Relate this to height of the water in the bottle.
Does the width of the bottle affect the pitch?
Now blow across the top of a bottle.
Is the note the same as when you tapped the bottle?
Vary the amount of water in the bottle.
Do the notes change the same way as when you tapped against the bottle?
Is it the column of air above the water or the column of water that determines the note?
Hint: think about the length of the vibrating column of air in a wind instrument.
Can you tune the bottles to play a scale of music?
Check your notes against a musical instrument.
26.2.3 Bunsen burner and trombone resonance
See diagram: 26.3.2.15: Bunsen burner resonance.
Experiments
1. Use two glass or hard plastic tubes 50 to 100 cm long with one tube diameter greater than a Bunsen burner tube, but less than the second tube.
Light the Bunsen burner.
Hold the smaller diameter tube vertically over the flame then move it up and down until you can hear a resonance sound.
Hold the greater diameter tube vertically around the first vertical tube.
You can move it up and down to change the pitch of the resonance.
The resonance is produced by the sudden expansion of air in the tube.
2. Place the Bunsen burner on the floor.
Light the Bunsen burner and adjust it to produce its greatest flame.
Use both hands to hold a 2m long cylindrical metal or cardboard tube vertically over the Bunsen burner, a few cm above the top of the flame.
Hear the acoustic resonance produced by a resonant standing wave in the tube.
Use tuning forks to estimate the pitch of the resonance.
Shorter tubes produce a higher pitch than longer tubes.
The diameter of the tubes do nor affect the pitch.
The frequency for an open tube = speed of sound / 2 × length of the tube.
Use a second tube with less diameter to fit inside the first tube, like a trombone, and vary the length of the tube over the Bunsen burner.
Use the "trombone" to show that the resonant frequency in an open pipe is lower for a greater length.
Column length in metres (m) and frequency (Hz): 0.2 m 440 Hz, 0.5 m 172 Hz, 1.0 m 86 Hz, 1.5 m 57 Hz, 2.0 m 43 Hz.
26.2.4 Drinking straw oboe and trombone
1. Pinch flat 1 cm at one end of a drinking straw.
Experiments
Cut off thin little triangles from each side so that the drinking straw has an arrow shape.
Put the straw far enough into your mouth so your lips do not touch the corners, but are around the round uncut part of the drinking straw.
Press gently with your lips on the straw.
Blow gently just past the cut.
Move the end of the drinking straw in and out of your mouth until you get a sound.
While you are blowing try to touch the cut ends with your tongue and feel them vibrating.
Slide a wider drinking straw or plastic tube over the drinking straw you are blowing into.
The second tube can be used to lengthen or shorten the length of column of vibrating air, just like a trombone.
If you do not get a sound, try keeping the cut ends together with your tongue and blow again.
If you still do not get a sound the cut ends may be too stiff.
Remove the straw and press the cut ends together or manipulate them to make them less stiff.
2. Hold two or more sheets of paper together and blow into one of their sides.
Hold your lips tightly together and blow through them to make a "raspberry" sound.
Play a comb wrapped in tissue paper or a gum leaf.
The vibrating surfaces of the lips, the sheets of paper act in the same way as the reed in many musical instruments.
The reed may be constructed of metal or cane in the case of woodwind.
The reed initiates the vibrations in each of these instruments' column of air.
26.2.5 Glass harmonica
See diagram 26.3.7: Glass harmonica.
Experiment
Use six light weight glasses.
Fill them with different amounts of water.
Dip you index finger in water then move it slowly around the rim of one of the glasses to create a sound.
Repeat the experiment with the other glasses.
Note that the tone of the sound depends on the amount of water in the glass, i.e. the volume of air in the glass above the water.
The sound has a ringing tone, but some people think it is a haunting sound and do not like it.
You could tune a set of glasses to make a musical instrument and composers have written music for the glass harmonica.
26.2.6 Humming paper tube
See diagram 26.3.2.13: Humming paper tube.
Experiment
Use a 20 cm square piece of paper.
Cut off one corner.
Cut two notches in the opposite corner.
Roll the paper diagonally to make a tube about as thick as a pencil.
Fold the notched corner to cover the opening.
Suck through the tube.
You can hear a humming sound.
The paper corner outside the notches is drawn in then starts to vibrate slowly making a deep note.
26.2.7 Reed vibrations
See diagram 26.6.2.4: V-shaped point on the end of a straw.
Reeds made of cane and can vibrate by themselves, but attached to a musical instrument they can be forced to vibrate at the natural frequency of the air in the tube.
The reed closes at lower air pressure and opens at higher pressure, so the air stream from the lungs of a player can sustain the vibration of the air in the musical instrument.
Experiments
1. Make a double reed from a plastic drinking straw, cut a V-shaped point on the end of the straw as in the diagram.
Put the cut end in your mouth, squeeze slightly with you lips and blow into the reed.
Vibrating surfaces act in the same way as the reed in many musical instruments.
2. Hold two sheets of paper together and blow into one of their sides.
Hold your lips tightly together and blow through them to make a funny sound.
3. Play a comb wrapped in tissue paper or a leaf.
The reed starts vibrations in a musical instrument's column of air.
For the human voice, the vocal cords in the throat act as a double reed and are set in motion by air exhaled from the lungs.
4. Cut a 2 cm piece from a plastic drinking straw.
Press one end together.
Cut it to a point.
Put it against the front of your top palate.
Make musical sounds when you blow through it.
The pointed tongues of the straw vibrate rapidly as the air passes through the piece of straw to make a high note.
Many musical instruments are based on this principle of a vibrating reed, e.g. clarinet.
5. Blow different lengths of drinking straws.
Flatten 2 cm of the end of a straw.
Cut off the end corners.
Use your lips to hold the end of the straw flat.
Blow into the straw to make a sound.
Do not blow too hard or you may hyperventilate (too much oxygen to the brain).
If you feel dizzy breathe into a paper bag for a few minutes.
Cut other straws to different lengths.
Blow into each to make a sound and arrange them in order from low to high pitch.
Observe the lengths of the straws and the pitch of the sound.
26.2.8 Resonance in aluminium pipe
The vibration of a pipe, caused due to being knocked, may drive the wave motion of the air inside the pipe.
The wave motion transfers and reflects so that standing wave forms inside the pipe.
This is the principle of wind instruments, e.g. a flute.
Its pitch may change through adjusting the standing waves of the air column inside the pipe.
Experiment
Use a 1 m long, 2.5 cm of diameter, aluminium pipe.
Hold the middle of the pipe horizontally with your thumb and index finger.
Knock the pipe on its middle as hards as possible with a golf club.
Listen to the sound of the pipe.
Measure the pipe, from its middle to the two sides, separate 13 cm, 25 cm, 35 cm and 39 cm.
Mark these positions on the pipe with a sharp pencil.
Note that the positions marked are approximate.
Real exact position must be dependent on the resonance of the pipe.
Press some point on the pipe and knock it with the golf club.
If the pipe may sound the pure resonance, the point is the exact position.
Hold the pipe at the points marked separately with your thumb and index finger vertically, then knock it with the golf club.
Listen to the sounds and record them.
Holding the pipe and knocking it causes its vibration so that a wave column, i.e. a standing wave, forms inside the pipe.
The standing waveform depends on the position at which the fingers hold the pipe and the position knocked.
The positions are different, the waveform is different and the frequency of the sound is different.
When you knock the pipe at 25 cm from the middle of the pipe, the pitch is the lowest (viz. the frequency is the lowest.)
When you knock the pipe at 13 cm and 39 cm from the middle of the pipe, the pitch is the highest (viz. the frequency is the highest.)
The two ends of the above pipe are open.
At the open ends the incident wave and the reflected wave are in phase with one another, so the vibrations of the air at the ends are strengthened.
Thus both of the two ends are the antinodes of the standing wave.
Hold the pipe at different position and knock it thus the amount of the standing waves are different so the pipe may sound different pitches.
The more the standing waves, the higher the pitch of the pipe.
Find the best positions to be knocked and the points at which the pitch of the pipe is the highest and lowest by the same way.
If you plug up one end of the pipe, at the end, the incident wave and reflected wave are out of phase [having opposite phase].
The point is the node of the standing wave.
26.2.9 Resonance in paper pipe or drinking straw
1. Use paper, scissors, tape, pencil.
Cut a 15 cm × 15 cm square of paper, and roll it tightly diagonally around a pencil.
Use adhesive tape on the centre to hold it together.
Remove the pencil.
At one end, cut in the corner of the V one third of the way in, on both sides.
If you do not cut right from the corner of the V it will not work.
Fold the triangular end that you have marked down, and press it gently onto the pipe to make it airtight.
Place the other end of the tube in your mouth, and suck gently.
The triangle will vibrate sounding like a whistle.
Make different sizes of paper pipes and note how the sound varies.
Note whether it makes the same sound whether you blow gently or hard.
26.2.10 Slide whistle, piston, flute
See diagram 26.3.2: Slide whistle.
A slide whistle is a short duct cylindrical flute with a sliding piston and handle so is closed at one end.
Experiment
Blow on the slide whistle at different piston lengths.
26.2.11 Wind instruments resonance
Resonance Kundt's tube, (Commercial).
"Singing rods", resonance in open rods (toy product)
See diagram 26.3.01: Resonance in air columns.
See diagram 26.3.2.1: Standing waves in a flute.
See diagram 26.3.02: Reservoir-resonance tube apparatus.
Wind instruments, e.g. pipe organs, flutes, oboes, clarinets, produce their musical sounds by resonating standing waves in air columns.
The air columns are in tubes either open at both ends or closed at one end.
In a trumpet the player's lips vibrate in a cup-shaped mouthpiece, but in a clarinet or oboe air is blown between pieces of reed to cause them to vibrate.
Standing (stationary) waves can occur in air columns where a tube is closed at one end.
For example. flute, pan pipes, or in air columns, where tube is open at both ends, e.g. open organ pipes, saxophone, trumpet.
In a flute or recorder, the player covers or uncovers holes to change the length of the vibrating air column.
The player of an oboe blows air between two reeds joined as a mouthpiece, so they vibrate against each other to produce a standing wave in the instrument.
Nodes refer to longitudinal standing (stationary) waves in air columns that always have a node at a closed end and an antinode at an open end.
Antinodes formed by standing waves in air columns at the open ends of any tube are in located a small distance beyond any open end, called the end correction.
As the instrument is played, the air in the resonating column becomes warmer and moister.
Consider the effect of extended playing of a reed instrument such as a saxophone or oboe will have on pitch.
How might these changes affect the total sound that an orchestra produces?
How would musicians avoid these problems?
Experiment
Cut three small slits along the length of the straw about 2.5 cm apart.
Cover one of them and blow as before.
Separate the slits so they form small holes.
Then cover two, then three each time you blow.
Put three fingers of the left hand on the farthest three holes and three fingers of the right hand on the nearest three holes.
The length of the air column vibrating to form a sound is as long as the nearest open hole.
26.3.01 Sonometer, single string monochord, Mersenne's Law
See diagram 26.3.1.9: Monochord.
See diagram 26.3.2.3: Staff notation of the major diatonic scale.
1. The first recorded monochord was invented by Pythagoras, (570-500 BC).
He observed that the different musical notes from blacksmiths striking anvils with hammers depended on the weights of the hammers.
He invented a monochord, consisting of a stretched string over a sounding board with one end attached to a scale pan.
The tension in the string depended on the weights in the scale pan.
From these observations he devised the scale of eight notes, the octave.
2. The monochord is a hollow wooden sounding box with a wire whose length of vibration is adjusted by movable bridge B.
Adjust the tension in the wire with weights D.
Pluck the wire between A and B at the centre so that the wire between the bridges starts to vibrate and emits a musical note of definite frequency.
Change this frequency by changing the load so as to change the tension in the wire or change this frequency by changing the distance between bridges A and B.
Use a tuning fork to "tune" the sonometer to a sound of known frequency.
Use the thickest guitar G-string (0.4064 mm) (0.016 inch).
Start with slotted brass masses, up to 500 g, then use 0.5 kg masses, so you can increase the mass in 0.5 kg increments up 3 kg to give a tension of 4.9 N to 49 N.
3. Mersenne's Law (Marin Mersenne, 1637, France):.
The fundamental frequency of a vibrating string is proportional to sqrt tension and inversely proportional to the length and sqrt mass per unit length.
Equations for the vibration of a stretched string.
* For a string under constant tension, the fundamental varies inversely as the length of the string,
* For a string of constant length, the frequency is proportional to the square root of the tension, (the stretching force),
For example, as you tighten a guitar string the pitch, (sound frequency), increases.
* For a given length and constant tension the frequency varies inversely as the square root of the mass / unit length,
For example, thick guitar strings wound with copper produce a lower frequency than the lightweight steel or nylon strings.
Experiments
4. Hear the same pitch
Sound the fork and wire alternately and adjust the wire until you hear the two notes emitted to be equal in pitch.
5. Listen to beats
When two notes of nearly equal frequency are sounded simultaneously you hear a regular throbbing noise called beats.
The frequency of the beats is equal to the difference in frequencies of the two notes.
Sound the tuning fork and wire simultaneously, adjust the wire so the beats become slower then disappear, because the wire and fork have the same frequency.
The fundamental note of the vibrating air column depends upon its length so you can tune an air column to a tuning fork altering its length.
6. Oscillating frequency of a string is dependent on the tension acting on the string and the length of the string.
Prepare a strip of wooden board.
Nail two pieces of short boards on either end of the wooden board.
Place the board flat on a level tabletop, the two short boards below so that the middle of the wooden board is in the air.
Draw a straight line on the wooden board.
Screw three screws with the same sizes on the board.
Prepare a piece of long nylon string.
Tie the string to the two screws at the two ends of the wooden board.
Adjust the direction of the groove on the top of the middle screw so that the string goes through the groove.
Screw the screws at the two ends of the wooden board to tighten the string.
Be careful not to make the string too tight.
Strike the string to make it emit a sound with a pitch.
Screw one of the screws at the two ends to make the string tighter.
Strike the string.
Repeat the above steps several times and listen to the sounds and compare the change in pitch.
You may find that the tighter the string, the higher its pitch, when its length does not change.
Insert a small board under the string so that the length of the string is changed.
Also, place a knife or a pencil under the string.
They may separate the string to change its length.
Strike the string and compare the change in pitch of the string.
Repeat the above steps.
Summarize the relationship of the length of the string to the pitch.
You may find that the shorter the string, the higher its pitch, when its tension does not change.
Prepare an open mouth plastic box instead of the above wooden board.
7. Prepare a glass stick of 80 mm length.
Insert it under the string.
Strike the string.
The sound changes strongly obviously.
Every stringed instrument, such as a guitar and violin, has a gut made up of a wooden box.
It may enhance the sound and make the string sound partial tone that is producing resonance.
So the wooden box is also called a resonating box.
26.3.1 Paper rider method, fundamental of string
See diagram 26.1.12: Pitch and tension.
See diagram 26.2.1.2: Finger on string.
Experiments
1. Paper rider thrown off by resonance: Put a small piece of paper, "paper rider", on the wire midway between the two bridges of a sonometer, A and B.
Strike the tuning fork to set it vibrating and place the end of the handle firmly on the hollow wooden box of the sonometer.
If the fundamental note of the wire has the same frequency as the tuning fork wire will start vibrating resonance and the paper rider thrown off.
2. Cut a cardboard into a paper horse.
On the paper horse drill a hole at some point, higher than its gravity centre.
As before, make the string resonate with the tuning fork and a standing wave forms on the string.
The paper will move when the resonance occurs.
When a standing wave forms on the two fixed ends of the string, the two ends must be nodes of the wave and the antinode must be between the two ends.
If the wave caused by the tuning fork is fundamental, the amplitude of the paper horse may reach the maximum.
3. Drop a V-shaped paper rider over the vibrating string of a stringed instrument, e.g. a violin string, and observe the resulting motion.
26.3.2 Piano string resonance
Place a heavy object on the soft pedal of the piano to release the dampers.
Open the lid at the top of the piano and talk into the gap between the strings and the back of the instrument.
When you talk to the piano, does it answer back?
Play some different musical notes into the piano.
How does it respond to high notes and to low notes?
Which parts of the piano are responding to the sounds you are making?
Investigate the strings in the back of a piano or on a guitar.
Note the changes in pitch that come from different thickness, tension or length of the strings.
Consider what effect extended playing of a stringed instrument may have on pitch.
Note that as the instrument is played the temperature of the strings increase.
26.3.3 Pitch and mass (density) of vibrating strings
See diagram 26.3.1.10: Pitch and mass (density).
Pitch depends on the length, tension and thickness of the vibrating string.
Experiments
1. Use rubber bands of various sizes and masses, an empty box or container.
Pluck each band separately, and note their pitch.
Cut out one large side of the box or container.
Stretch rubber bands of different sizes around the box.
Adjust the bands so that each has the same tension as near to possible.
Note how does increasing mass of the band change the pitch,
Strike the strings one by one.
Note their pitches.
In addition using weights hanged to do similar experiment.
Use a wire and a rubber tape with the same length.
2. Use two same kegs full of sand.
Hang the two kegs with separate wires and rubber tape.
The wire and the rubber tape have the same inner tension as they hang weights with the same weight.
Strike the wire and the rubber tape separately.
Compare the difference in pitch.
You may find that they sound lower than the above experiment, because the keg can plays an important role of a resonance box besides as a backstop.
Their pitches are dependent on their mass or the density of the string, exactly.
The denser the string, the lower its pitch and vice versa.
26.3.4 Plastic bottle guitar, stringed instrument
See diagram: 26.3.1.11: Plastic bottle guitar.
Experiments
Insert two nails side by side into one end of a piece of softwood timber 300 mm × 25 mm × 15 mm.
Tie a length of fine wire to each of the nails and hammer them into the timber.
Screw two screw eyes side by side into the other end of the timber.
Cut rectangular holes in opposite sides of the plastic bottle near its base so that you can push the timber through the holes with the nails and wire poking through.
Pull the wires tight and tie the other ends to the screw eyes.
Adjust the sound of the strings by screwing the screw eyes to tighten the wires.
Insert a small wooden bridge between the wires and the base of the plastic bottle.
26.3.6 String vibrates at constant length
If a string vibrates at constant length, the frequency n is directly proportional to the square root of the tension T, i.e. n is proportional to T.
Use a 1.5 kg load.
Move bridge B to adjust the length AB, L, of the vibrating string until it vibrates with the same frequency as the lowest frequency tuning fork.
Use the paper rider method or the beats method.
Record the load, T, and the frequency of the tuning fork, c.
Mark the position of bridge B and do not change it.
Use the tuning fork of the next highest frequency.
Adjust the tension in the wire, T, until the frequency of the sound from the wire is the same as the frequency of the tuning fork, c.
Repeat the experiment for all other tuning forks and record the values of n and T.
Plot a graph of n (y axis) against T (X axis).
If the points on the graph are in a straight line passing through the origin, n is proportional to T.
26.3.7 String vibrates at constant tension
If a string vibrates under constant tension, the frequency n is inversely proportional to the length, L, i.e. n is proportional to 1/L.
1. Move bridge B so AB, L, = 80 cm.
Adjust load, T, until note from wire is same as note from tuning fork.
2. Keep tension of wire constant, find lengths AB, i.e. L, vibrating with same frequency as tuning forks with frequencies, e.g. 256, 320, 384, 426, 512 c.p.s.
Use the paper rider method or the beats method.
Plot a graph of n, cycles per second (y axis) against 1/L, cm (x axis).
If points on the graph are in a straight line passing through the origin, n is proportional to 1/L.
26.3.8 Violin strings and piano strings
A violinist draws the bow across the string at about 1 / 7 of the length from the end to produce overtones and harmonics.
Also the string can be plucked there to produce pizzicato.
The four strings produce the musical notes E, A, D and G.
The piano uses 88 keys to strike the 230 steel wire strings under a tension of about 70 kg near the end.
26.4.01 Sound, sound waves, reflection, refraction, diffraction
Sound is a form of energy.
Sound energy moves by longitudinal waves.
The molecules in the air vibrate back and forth, crashing into the molecules next to them, causing them to vibrate.
All sounds come from vibrations.
Sound is produced by a vibrating source that then travels through substances.
Sound cannot travel through a vacuum.
Sound is the sensation perceived the ear by the vibration of the surrounding air or any other medium, e.g. ear pressed on wood.
Infrasound and ultrasound refers to pressure waves outside the range of audible frequencies, so not heard by the human ear.
A sound synthesizer stores sound waves electronically as a binary code, which can later be converted to a variable electric current that controls a loudspeaker.
1. Sound waves reflect - echoes.
2. Sound waves refract towards the normal when moving from a less dense medium to a more dense medium where their speed is slower.
Sound wave refraction is not obvious as with light.
It occurs during the "cool lake effect".
During the day you see, but cannot hear cars moving on the other side of the lake.
During the night a temperature inversion occurs.
The temperature is coolest over the lake, but warmer with increase in height.
Speed of sound also increases with height so part of the sound wave closest to the ground travels slower, and part of the wave above the lake is travelling faster.
So the sound wave changes direction and bends downwards and you can hear the cars moving on the other side of the lake.
Sound wave refraction has been likened to a toy car on a hard floor approaching carpet from left to right at an angle not equal to 90o.
The front right wheel reaches the carpet first and slows turning the toy car towards the normal.
Similarly, a tractor with separate front wheel brakes can turn to the right if the right wheel brake is applied.
3. Sound waves diffract with longer wave lengths diffraction more than shorter wavelengths.
3.1 Sound waves can diffract around small obstacles.
You cannot see a person in front of you, because something is in the way, but you can hear the person talking, because the sound waves diffract around it.
3.2 Sound waves can diffract through small holes.
You cannot see people inside a house, but you can hear them if a window is slightly open.
To soundproof a room you must seal it to prevent any sound passing though holes in the walls.
4. Sound waves form interference patterns, e.g. beats.
Thunder from nearby lightning strike has a sharp cracking sound, but has a rumble sounds at a distance as the longer wavelengths refract.
26.4.1 Cellophane noise vibrations
People watching movies used to complain about other people noisily opening sweets in cellophane wrappers!
Experiments
Use a piece of cellophane 5 cm square.
Stretch it tightly between the thumbs and index fingers of both hands.
Hold your hands in front of your face so the cellophane is in front of your lips.
Blow hard and fast at the edge of the tightly stretched piece of cellophane.
Keep your lips close together.
You must send a thin stream of air right at the edge of the cellophane.
Can you hear a noise?
When the air hits the edge of the cellophane, you will make a scream.
If you do not change the distance between the cellophane and your lips until the air hits it just right.
The fast moving air from your lip makes the edges of the cellophane vibrate.
Because the cellophane is very thin, the jet of air makes these vibrations very fast,
The faster something vibrates the higher the tone it creates.
26.4.2 Comb resonator, amplify sound from comb, chimes
Experiments
1. Hold a comb in the air and strike the teeth of the comb with your nail.
Ask another student to listen to the sound at a certain distance from you.
This student hears the reference sound and must compare this sound to all the following sounds.
Repeat the experiment by holding the comb firmly and vertically on a wooden table.
Strike the comb with the same force as before.
The surface are of the vibrating object, i.e. comb and table top, has increased, so the sound is louder.
Repeat the experiment, but strike the comb with a stronger force.
The larger the magnitude of the force striking the comb, the larger the amplitude of the vibration of the sound source.
In other words, the larger the energy of the sound source, the large the amplitude of the vibration received, the louder it sounds.
The amplitude of vibration of the comb teeth has increased so the sound is louder.
Repeat the experiment at different distances from the hearer.
For the same sound source, the farther the sources the lower the sound heard, because the less the energy distributed to the ear the lower the intensity of the sound.
2. Repeat the experiment with the comb held against a small wooden box.
A wooden box is best for making a sound amplifier, because it has the best resonance effect.
So the bodies of guitar and violin and the sound box of loudspeaker are made up of wooden material.
26.4.3 Drink-can to amplify the sound of a thread
Use a 1 m long, thick, silk thread or fishing line.
Rub the thread with a block of rosin.
Lift one end of the thread and let it fall free.
Listen to the sound of the thread.
Use an empty drink-can.
Punch a hole, slightly thicker than the thread, on the bottom of the can.
Insert one end of the thread into the hole and tie the end to a short pencil.
Lift another end again and let the can fall free.
Note the sound of the can.
Rub the thread down with your hand.
Note the sound from the can.
26.4.4 Insect footsteps in a paper bag
Trap a housefly in a smooth paper bag, seal it, and hold it horizontally above your car.
If you are in a quiet room you can hear the patter of the six legs and other rather curious noises quite clearly.
The paper behaves like the skin of a drum.
Only the tiny legs of the insect beat on the bag, but it begins to vibrate and transmits a loud noise as if a large animal was in the bag.
26.4.5 Knocking on bottles, blowing over bottles
See diagram 26.3.1.6: Bottle sounds.
See diagram 26.3.01: Standing waves in tubes closed one end.
1. Use 3 identical empty bottles, 1/3, 1/2 and 2/3 filled with water.
Lift each bottle by the neck and strike with a stick.
The bottle and water vibrate so the more water in the bottles the lower the pitch.
So the sound from the 2/3 filled bottle has the lowest pitch.
2. Repeat the experiment by putting your lower lip on the mouth of each bottle and blowing gently.
The air above the water in the bottles vibrates to make a sound.
The larger the amount of air in the bottle the lower the pitch.
So the sound from the 1/3 filled bottle has the lowest pitch.
3. Repeat the experiment by filling the bottles with equal volumes of heavy oil or water or kerosene.
Lift each bottle by the neck and strike with a stick.
The bottle and added liquid vibrate so the heavier the bottle and contents the lower the pitch.
So the sound from the bottle containing oil has the lowest pitch.
4. Repeat the last experiment by putting your lower lip on the mouth of each bottle and blowing gently.
The air above the water in the bottles vibrates to make a sound.
The larger the amount of air in the bottle the lower the pitch.
All bottles contain the same volume of air so the sounds from the three bottles have the same pitch.
26.4.5a Knocking sounds
Place an empty beaker on several pieces of paper.
Knock the beaker side gently with a glass stick to emit a harmonic sound like "jow", the sound of a bell.
Place a china dish instead of the beaker on the paper then knock it with the glass stick.
It sounds very long and pleasant to ear.
Polish a flowerpot with a piece of sand paper.
It emits very loud noise.
Many people try to cover their ears when they hear the sound that they do not want to hear.
Use two pieces of hard foams.
Press them together then rotate them at the opposite directions.
It may emit noise too.
Inflate then puncture it with a nail.
A shocking "bang" sounds suddenly.
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.
26.4.7 Sea wave patterns and sound wave patterns
See diagram 4.93: 1. Sea wave patterns 2. Sound wave patterns.
1. A Ocean wave, B Boat wave, C Ripples, D Combination wave
2. A Pure note, B Different frequencies combined
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.
26.4.8 Seeing and feeling vibrations that make sound waves
See diagram 4.97.1: Stretched rubber band.
Experiments
1. Stretch and pluck rubber bands and the strings of string instruments.
2. Hold a ruler on the edge of a desk with 15 cm extending over the edge and pluck it.
3. Put a drum on a desk and scatter puffed cereal grains or pieces of tissue paper or cork across the top.
Strike the drum and watch the vibration.
4. Press the thumb and forefinger against the larynx and make a low-pitched sound with the voice.
Feel the "own sound" vibration.
5. Hold a tuning fork loosely by the handle and strike the prongs against the edge of the desk.
Note what you hear.
Again, strike the prongs and quickly touch water in a pan with the tips of the prongs.
The vibrating fork splatters the water.
26.4.9 Sound cannot travel through a vacuum
See diagram Bell jar with spigot.
The speed of sound in air at 0oC = 331 ms -1.
Experiment
Use an aspirator or simple vacuum pump to pump the air from a bell jar fitted with a spigot.
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 container or bottle and shake the bell while the container fills 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 container.
Shake the bell again.
The sound of the bell is not as loud as before, because sound cannot travel through a vacuum.
26.4.10 Sound waves travel through wood
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.
26.4.11 Tap different containers
Railway workers used to tap train wheels to find if they had developed faults.
The faulty wheels sounded different, because they contained cracks.
Experiments
1. Listen to the sound each makes.
Can you hear any differences?
Sort the containers by quality of sound.
Listen for a good ringing sound and a flat sound.
Next examine the containers in each group.
Which group contains the cracked containers?
26.4.12 Timbre, quality
Timbre is the distinctive quality of a musical note or voice although having the same pitch and intensity.
Timbre is caused by extra small waves called harmonics that add quieter sounds to the main sound of the instrument.
A voice lacking timbre sounds like a monotone.
Different musical instruments may play the same note, but they sound different because they have this different quality.
26.5.01 Tuning forks
Sound, tuning forks, (Commercial).
See diagram 26.191: Wave pattern of a tuning fork.
See diagram 26.1.1: Vibration of tuning fork
Experiments
Hit the tuning fork on the knee or ball of the hand.
Do not hit on metal, because if tuning forks become chipped they change their inertia and will vibrate at different frequencies.
Put your arms straight above your head and clap to show proper motion of a tuning fork.
Remove unwanted vibrations by touching gently near the joint after striking the fork.
The vibrating tuning fork should be almost silent when used.
Hold the tines near the ear to hear it clearly.
Spin the tuning fork as you listen and observe that it is loudest between the tines by constructive interference.
26.5.1 Beats with two tuning forks
See diagram 26.8.6: Loaded tuning forks.
Superposition of sound waves of similar frequency produces pulsation called beats.
Beats 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. 2 beats per second will occur with combined frequencies of 200
Hz and 198 Hz.
Experiment
Use two identical tuning forks.
Load one of the tuning forks with a piece of adhesive tape to change its natural frequency of vibration.
Strike both tuning forks and hear the "beats".
26.5.2 Beats from heated tuning forks
The beating frequency is the difference between the interfering frequencies, the note you hear is the average of the two original frequencies.
Heat one of a pair of two identical aluminium tuning forks.
Heating reduces the Young's modulus of the aluminium, so the vibrations no longer match when the tuning forks are struck.
26.5.3 Forced vibration from tuning forks
A tuning fork struck while held in your hand produces little sound, but placed on a box or overhead projector they vibrate at the same frequency of the tuning fork.
Also, they produce more sound, called forced vibration.
Demonstration tuning forks are mounted on a sound box to allow for forced vibration of most large glass or wooden objects.
These objects have so many resonance frequencies that any tuning fork will cause them to resonate.
Similarly, a guitar has a sound box, and why a piano string is attached to a sounding board.
A louder sound is always produced when an accompanying object of greater surface area is forced into vibration at the same natural frequency.
Forced vibration at natural frequency causes resonance, high amplitude oscillation.
A set of four different tuning forks mounted on resonance boxes make the musical scale.
26.5.4 Frequency of tuning forks with a sonometer
See diagram 26.3.1.9: Sonometer, monochord.
1. Find the frequency of a tuning fork with a set of tuning forks of known frequencies.
Adjust tension of wire, T, to same value.
Find the length AB, L, of the string under the same tension until note from wire is same as note from the unknown tuning fork.
From the graph locate L and the corresponding value of the unknown frequency.
2. Find the frequency of a tuning fork using no other tuning forks.
Use a 2 kg load.
Move bridge B to adjust the length AB, L, of the vibrating string until it vibrates with the same frequency as the unknown frequency
tuning fork, using paper rider method or beats method.
If L > 25 cm increase load and repeat the experiment.
Record length L cm of the vibrating wire, and load, T.
3. Cut length L from a reel of wire the same as used in the sonometer.
Find its weight, M.
The frequency, n, of a length L cm of wire, of mass per unit length M g/ cm under a tension T, =
1 / 2L T / m cycles per second.
26.5.5 Reflection from tuning forks
Reflect light from the end of a tuning fork with a small mirror attached to allows inspection of the motion of the tines fork by amplifying it as the reflected light.
Also, the light beam can be seen in a smoky room the light beam.
26.5.6 Test for materials that absorb sound with tuning forks
Test the sound absorbing properties of small pieces of rubber, sponge, felt, and other materials.
Place the piece to be tested on a wooden table top, strike a tuning fork, and bring its handle down on a piece of material.
Then strike the tuning fork again and touch its handle on the bare wood top.
Which is louder?
26.5.6a Tuning forks make a pure note when struck and allowed to vibrate.
This note is of just one frequency and is called the first harmonic of that frequency.
A musical instrument playing the same note makes not only the pure note of the tuning fork, but also other notes called harmonics.
Harmonies are notes whose frequencies are an integral number of times the frequency of the first harmonic.
Thus the second harmonic is twice the frequency of the first.
It is the combination of many harmonics that give musical instruments their distinctive sound.
Tap the tuning fork and listen to the sound it makes.
Now play the equivalent note on a piano or other musical instrument.
Do they sound the same?
How do the sounds differ?
26.5.7Tuning forks move ping-pong balls
See diagram 26.3.3.5: Tuning fork moves ping-pong ball.
Fix two identical tuning forks on two identical resonance boxes.
Hang a ping-pong ball from the arm of a stand with a string, so that it just touches a tine of one tuning fork.
Place the resonance boxes mouth to mouth.
Use a rubber hammer to knock another tine of the tuning fork, not touching with the ping-pong ball.
Observe the change in motion of the ping-pong ball as it starts to vibrate.
It changes from being at rest to vibrating, showing that it has gained energy.
The knocked tine of the tuning fork, as a sound source, causes the change in motion of surrounding medium.
26.5.8 Tuning forks in strobe light
Place a large tuning fork in front of an adjustable strobe light.
Adjust it to make the vibration appear slower or stop.
The strobe must match the frequency of the tines.
The difference between the strobe rate and the tuning fork frequency determines the perceived rate of vibration.
26.5.9 Tuning forks with oscilloscope
Oscilloscope (Commercial).
Verify the frequency of the tuning fork with an oscilloscope.
Hook a speaker removed from its housing to the leads of the electroscope, using a BNC connector with a probe, or use a microphone.
Hold the tuning fork up to the speaker, adjust the settings to see that the tone of the tuning fork is a pure curve, compared with human voice or musical instruments.
26.5.10 Tuning forks with same frequency
Tuning forks that are not the same frequency will not resonate.
Two tuning forks that are the same frequency can be made to resonate audibly if the vibration is loud enough.
26.5.11 Sound wave patterns of tuning forks, waveform of tuning forks
See diagram 26.1.2: Harmonics.
See diagram 26.191: Wave pattern of a tuning fork.
See diagram 26.1.1: Vibration of tuning fork
A tuning fork is bar of steel shaped like a U with a handle.
Experiments
1. Strike a prong of the fork lightly struck on a suitable surface, e.g. felt pad or rubber bung.
Put the handle in contact with a wooden surface and you hear a pure note of constant frequency.
This frequency is usually stamped on the handle of the tuning fork.
But if you strike the tuning fork on a hard surface, e.g. the bench, you hear an impure note.
2. Examine a set of vibrating tuning forks.
Note how do their lengths and thickness correlate with their pitch when struck.
3. The best place to strike a tuning fork is about 1/3 of its length from the tip to get a clean fundamental note.
4. With a few drops of hot sealing wax attach a piece of fine wire to the prong of a tuning fork.
The fork is held rigidly by the handle and placed horizontally just above the table top.
Smoke a small pane of glass over the flame of an oil lamp or a candle.
Lay the smoked glass pane under the prong with the fine wire bent to touch the glass pane.
Start the vibrations with the finger and draw the pane along the table fast enough to make a wavy line on the pane.
5. Repeat this experiment drawing the pane away at different speeds and using different tuning forks.
6. Describe the graph of the amplitude of the tuning fork against time.
Attach a short thin stiff wire to the end of a tuning fork with drops of candle wax.
Prepare a stand and a table of fit height.
Fix the tuning fork on the stand, making sure the tuning fork is just above the tabletop.
Use a block of glass board and blacken one side of the glass board by fuming it with the smoke and fire of a candle.
Place the glass board under the tuning fork, the black side upwards.
Bend the thin lead to make its peak touch the glass board just.
Now the tuning fork is at rest.
Pull the glass board and the lead draws a straight line on the glass board.
Strike the tuning fork to start its oscillation.
Pull the glass board at constant speed.
The lead draws the waveform on the glass board.
See the lower diagram.
7. Repeat the experiment, but pulling the glass board at different speeds or using different tuning forks.
26.5.12 Speed of sound in air and frequency of tuning forks
1. Find the velocity of sound in air at room temperature using the closed resonance tube.
The closed resonance tube AB is a tube of wide, uniform bore, open to the atmosphere at A, but closed by a water surface at C.
The length of the air column AC may be varied by moving the reservoir R up or down or by moving AB up or down.
Record the room temperature.
2. Sound the tuning fork of highest frequency just above A to increase the length of the air column AC until the sound emitted is at maximum loudness.
Now the fundamental frequency of the air column is equal to the frequency of the tuning fork.
3. Record length L1 cm of the air column.
Increase AC until you hear a second point of resonance lower down the tube.
4. Keep the tuning fork vibrating and record the new length L2 cm of the air column AC.
Record the frequency n of the tuning fork used.
When resonance occurs at length AC = L1, then the column of air length (L1 + e) cm = λ / 4, λ = wavelength of the tuning fork.
The column of air that vibrates is slightly longer than L1 and its extra length is called "e".
When resonance occurs at length AC = L1, then the column of air length (L1 + e) cm = λ / 4, where λ = wavelength of the tuning fork.
When resonance occurs at length AC = L2, then the column of air length (L2 + e) cm = 3 × λ / 4.
L1 + e = λ / 4
L2 + e = 3 × λ / 4
(L1 + e = λ / 4L) - (L2 + e = 3 × λ / 4) = λ / 2
Velocity of sound = frequency × wavelength, v = n × λ
v = 2 × frequency (L2 -L1) cm / second
5. Knowing the value of the velocity of sound in air, find the frequency of the tuning fork.
26.5.13 String resonates with tuning fork
The earliest stringed instrument was perhaps the Greek lyre, some being strings stretched on the shell of a tortoise.
Stringed instruments have stretched strings that vibrate when plucked or when a horse hair bow slides across them.
The strings of a violin are stretched across a wooden bridge that conducts vibrations into the sound box.
It resonates to give a louder sounds with different characteristics.
Piano strings vibrate when hit with hammers covered in felt controlled by the keys of the keyboard.
Experiments
See diagram 26.3.1.9: Sonometer, monochord.
1. Use a board, a pulley, some weights, two ball point pens, a tuning fork, a piece of string.
Fix one end of the string on the board and another one is tightened by the weight through the pulley.
Insert the two ball point pens between the string and the board.
Strike the tuning fork to start its oscillation and let it touch the board.
Does the string vibrate to sound?
Add the weight to adjust the tension of the string, or remove the ball point pens to change the length of the string,.
Do this so that the the string vibrates at the frequency of the tuning fork and its amplitude and loudness reaches the maximum.
The string resonates with the tuning fork and a standing wave forms on the string when the frequency of the string matches the frequency of the tuning fork.
2. Change the position of the ball point pen to change the fundamental of the string slightly.
Strike the tuning fork and the string at the same time to make them sound.
Listen to the sounds.
You may hear each vibration and the slow and steady sound of "pat".
Adjust the position of the ball point pens so that the frequency of the "pat" sound is slower and slower.
It finally disappears when the string resonates with the tuning fork again.
When two vibrations with similar frequencies exist at the same time, each of their sounds may be heard.
Also, they may be superposed to form a slow and steady frequency, named "pat".
The frequency of "pat" is the distance of the two frequencies.
26.5.14 Wave patterns of a tuning fork
Waves, (Commercial)
See diagram 4.94: Wave patterns of a tuning fork:
A Fine wire, B Wax, C Smoked glass sheet on table, D Tuning fork not vibrating, E Base line, F Tuning fork vibrating.
Experiment
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.
26.5.15 Feel vibrations with a balloon
1. Hold a blown up balloon between your hands at a short distance from a radio speaker.
Feel the vibrations in the balloon.
2. Inflate the a large party balloon.
Turn the music on loud.
Place both hands lightly on the balloon.
Walk around the room while holding the balloon between your hands.
Feel the balloon vibrating more with lower notes.
3. Remove the top and bottom of a drink can with a can opener.
Make sure that no sharp edges remain on the rims.
Cut off the bottom of the balloon, open it slide it over one end of the opened drink can.
Attach a small mirror to the balloon.
Apply your mouth to the open end of the tin can.
Shine a light reflects on the mirror.
When you speak, the balloon moves the mirror, which moves the light.
4. Make drums by sliding the cut balloon over the opened drink can.
Put rubber bands around the can and across the top of the opened drink can.
Snap the rubber band on top of the can to make noise.
Observe vibrations of the balloon over the opened can.
5. Blow up a balloon.
Pinch the neck with both first finger and thumb, then pull apart while letting air escape from the balloon.
The balloon makes a high-pitched squealing noise with changes in pitch as you pull and release the neck of the balloon.
The escaping air molecules cause the rubber in the neck of the balloon to vibrate to make the squealing noise.
6. Release the air from the balloon and observe vibrations at the opening and note the pitch of the sound.
7. Repeat the experiment by making the opening wider and note the lower pitch of the sound.
26.5.16 Oscillation of object and production of sound
Fasten one end of an elastic or other elastic tape to a nail on a wall or the handle of a door.
Strain another end of the elastic with your hand and pluck the tightened elastic with a pencil.
Observe its oscillation and listen to its sound.
Repeat the experiment, but suddenly hold the oscillating elastic with your hand when hear the sound of the elastic.
The sound will disappear immediately.
26.5.17 Sound wave patterns, oscillations, origin of sound, tuning fork vibration
See diagram 26.190: Sea waves and sound waves.
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.
Experiment
1. Observe a boat passing over 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 ripples usually have an even higher frequency than the other two.
Now these three vibrations combine to form a pattern.
26.5.18 Vibrating desk, blackboard, chalkboard
1. Tap a pencil on the edge of a desk at different points along its length while pressing your ear to the desk
2. Strike a tuning fork on a hard surface and hold its stem firmly on the blackboard.
The blackboard will sing to the students!
26.5.19 Vibrating cereal grains
1. Put a drum on a desk and scatter puffed cereal grains, e.g. rice or pieces of tissue paper or cork on a drum surface or upturned loudspeaker.
Hit the drum.
Listen to the sound of the drum and observe the movement of the rice at the same time.
If no drum, place the sound box of a recording machine or acoustics level on a table, its right side up, instead of a drum.
Place several small pieces of paper on the cloth of the sound box.
Choose a piece of music with more bass and turn up the volume.
Observe that the paper oscillates along with the music.
2. Make some different sized drums by stretching tracing paper tightly across the mouths of the jars.
Fix the paper in place using rubber bands or a pieces of string.
Tap the paper lightly with a pencil to make a sound.
You cannot see the paper vibrate, but if you place rice grains on the paper and tap it again you can observe the vibration.
3. Observe how the size of the drum affects the sound made and the behaviour of the grains.
Make different sized drums by stretching greaseproof paper tightly across the mouths of the jars.
Fix the paper in place using rubber bands or a pieces of string.
26.5.20 Vibrating drums and balloons, ping-pong ball and tuning fork
1. Tape the string to the ping-pong ball and hang it touching one side of the drum.
Gently hit the other side of the drum and measure how far the ping-pong ball bounces off the side of the drum.
Repeat the experiment by hitting the drum harder.
2. Tape the string to the ping-pong ball and suspend it in a clear space.
Tap the tuning fork to set it vibrating and place it next to the ping-pong ball and observe its movement.
3. Touch the end of the tuning fork on the surface of a bowl of water.
Observe the movements in the water.
4. Inflate a balloon.
Use the first finger and thumb of both hands to pull out the neck to make a slit and let the air out of the balloon.
Observe the vibrations in the neck of the balloon.
5. Place an empty coffee tin on the palm of your hand.
Shout into its open top and feel the vibrations on your hand.
6. Make some different sized drums by stretching waxed paper tightly across the mouths of jars or other containers.
Fix the paper in place with rubber bands or string.
Tap the paper lightly with a pencil to make a sound.
Observe vibrations in the waxed paper.
Place rice grains on the paper and tap it again.
Observe the movement of the rice grains.
Note whether the size of the drum affects the sound made and the behaviour of the grains.
When you tap the drum or the tuning fork it vibrates.
As the vibrating surface moves in one direction it pushes molecules of air away from itself.
As it moves back in the other direction, pushing the molecules on its other side in the opposite direction, it leaves a "gap" on the first side.
In a sphere around the vibrating object, the molecules of air am alternately compressed and decompressed.
This produces compression and rarefaction in the air.
These compressions and rarefactions are longitudinal compression waves and produce sound.
Loudness or volume is determined by distance of the sound source from the ear, duration of sound and intensity of energy transmitted per unit area per unit of time.
26.5.21 Vibrating ruler
See diagram 26.1.3: Vibrating ruler.
Experiments
1. Hold a ruler on the edge of a desk with 15 cm extending over the edge and pluck it.
2. Place a ruler, or a steel saw blade, flat on the edge of a table and the ruler extends about 15 cm out of the edge vertically to the edge.
Press the end of the ruler on the table with your hand, press another one with another hand then suddenly leave your hand off it.
Observe its oscillation and listen to its sound.
Repeat the experiment, but suddenly hold the oscillating end of the ruler with your hand when hear its sound.
The sound will disappear immediately.
3. Use rulers of different length, material and thickness.
Hold a ruler firmly to the edge of a desk with one end overhanging.
Flick the free end of the ruler and listen to the pitch.
Change the length of the overhang and again flick the ruler.
Hold two rulers of different thickness or materials so that they both overhang the same distance.
Compare their pitches.
26.5.22 Vibrating speaker
Turn on a music player loud.
Observe the speaker it vibrating especially if there is a lot of bass in the music.
Put your hand on the speaker to feel the vibrations.
Put a bowl of water on top of the speaker to see the water vibrate.
26.5.23 Vibrating tuning fork touching water
1. Use a 128 Hz tuning fork to touch water, one tyne then both tynes.
Observe the surprising splash and sloshing caused by vibration in the fundamental vibration mode.
2. Hang a tuning fork with a thread.
Strike it to start its oscillation.
Then quickly let its lower end touch the surface of water in a basin.
Observe the phenomenon appearing on the water surface when the sound of the tuning fork starts.
Touch the tuning fork with your hand and observe the disappearance of the sound and the change on the water surface.
Dip your finger rhythmically into water and see the pattern of concentric vibrations.
3. Hold a tuning fork loosely by the handle and strike the prongs against the edge of the desk.
Note what you hear.
Again, strike the prongs and quickly touch water in a pan with the tips of the prongs.
The vibrating fork splatters the water.
26.5.24 Vibrations in bowls
Fill a glass bowl to such a depth that when you rub the rim of the bowl with your wet fingers clear note is produced.
Lower a lead sinker or ball bearing suspended by fine thread until the side of the bowl is touched.
The heavy object is flung violently outward.
Repeat the experiment by lowering the heavy object to touch a vibrating tuning fork.
26.5.25 Vibrations in wind harps, Aeolian harp
Wind harp vibrations occur in wooden resonating box with strings stretched across two sound bridges and tuned to the same deep note or different notes.
Sound is caused by vortexes as air passes around the strings, vibrates them to produce a chord rising and falling up and down the harmonic series as wind speed varies.
An aeolian tone is a musical note caused by an air vortex action on a stretched string in an air stream.
The sound occurs around "singing" power lines, car aerials and boat rigging during a gale.
The mythical Aeolus was the Greek ruler of the winds who lived on his island of Aeolia.
26.5.26 Vibrations of soap film
A soap film can be set into motion by a sound wave in a wide ranges of frequencies.
The vibration amplitude is large for all forcing frequencies.
This caused by mass distribution concentrated at the antinodes, as observed by interference fringes in monochromatic light.
Experiment
Make a soap film on a brass wire ring.
Hold it until the unwanted water drops away completely.
Look for the angle at which you can best observe the soap film.
Put the soap film at the place where it can be watched clearly and is closest to your mouth.
Constantly speak monosyllabic words loudly.
Observe the oscillation of the soap film.
You can see similar oscillations of window glass when a big truck passes.
26.6.0 Ultrasound
The human ear can detect sound waves with frequencies of about 20 to 20, 000 hertz.
This range is known as "sound", with infrasound below the range and ultrasound above the range.
Ultrasonics, supersonics, are vibrations with frequencies greater than 20 000 Hz.
Some animals can hear sounds in the ultrasound range, e.g. dogs, but the human ear cannot hear them.
Bats use sonar echoes to locate insects using sounds in the 20 to 50 kHz frequency range.
Some insects have developed bearings in this range so that they can take evasive action.
Bats that transmit at a higher frequency can catch smaller insects than bats that transmit at lower frequencies.
Dolphins use clicks of ultrasounds to locate shoals of fish.
Echoing ultrasounds are used in underwater sonar and to detect cancers and check on unborn human foetuses.
Different tissues reflect ultrasound differently so a computer can assemble a picture of the unborn baby.
High amplitude ultrasounds are used to clean metals, to fatigue test materials and to break up kidney stones.
This is similar to loud sounds causing avalanches on steep slopes.
Sonar echoes are used in ships to measure depth and detect under water objects.
ASDIC was an early form of sonar, an abbreviation for Anti-Submarine Detection Investigation Committee.
Short wave radio listeners use several scales to record the characteristics of the signal they hear from their loudspeakers and headphones.
For example: "SIO" Signal strength, Interference and Overall rating, "SINPO" with the addition of N and P for Noise and Fading.