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7 Hear the difference: sound

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More than just noiseSound in the human experience goes far beyond a sensory survival tool: it is a part of human culture, song, dance, prayer, ritual and entertainment. Not only do humans make an extraordinary array of sounds with their own bodies—for example, talking, singing, whistling and clapping—but they have also designed and developed highly specialised tools for making sounds, such as musical instruments. Sound is also used in medicine, engineering, fisheries, communications and architecture to solve problems and improve quality of life.

7.1 Sound waves as longitudinal waves

Sound is a mechanical wave caused by a vibrating source. The particles surrounding the source oscillate and the kinetic energy of the oscillation is transmitted through the medium as a longitudinal (or compression) wave. In longitudinal waves the direction of particle oscillation is parallel to the energy transfer, which is the propagation direction of the wave (Figure 7.1.2).

compression rarefaction

air molecule movement

wave direction

Figure 7.1.2 Sound waves are longitudinal waves.

Identify that sound waves are vibrations or oscillations of particles in a medium.

compression, rarefaction, source, pitch, resonance, volume, timbre,

echo, superimpose, reverberation, echolocation, path length difference,

standing wave, node, anti-node

Figure 7.1.1 Sound is part of human culture.

THE WORLDCOMMUNICATES

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A sound wave in air will cause the air molecules to oscillate and the air particles to move back and forth. At one point in the oscillation cycle, the air molecules are at high pressure, packed closely together or compressed. At another point in the cycle, the air molecules are at low pressure, spread apart or rarefied.

If we represent a simple longitudinal sound wave mathematically by using a sine wave, we assign the maximum positive value of the sine wave to the point of maximum pressure—the compression point in the cycle—and the maximum negative value of the sine wave to the point of minimum pressure—the rarefaction. The wavelength is the distance between two compressions (or two rarefactions).

Another way to represent the sound wave as a sine wave is to consider the displacement of the air particles from their equilibrium positions. The wavelength, frequency and period are still the same, but at positions of maximum compression or maximum rarefaction, the air particle displacement from equilibrium is zero. Conversely, positions of maximum or minimum displacement correspond to zero compression/rarefaction. In other words, the graph of displacement is 90° of phase behind the graph of pressure (Figure 7.1.3).

displacementpressure

Figure 7.1.3 Red closed circles show particles displaced in a longitudinal wave. Red open circles show their equilibrium positions. Positions of zero displacement (marked by vertical lines) correspond to maximum or minimum pressure and vice versa.

Therefore, we have two ways of representing a sound wave as a transverse wave—plotting either pressure or particle displacement—and the two approaches give different peak positions. However, whichever approach we use, we still accurately represent the amplitude, wavelength and period of the longitudinal sound wave in the transverse sine wave. Hence, each approach is valid.

SCREAM

Sound will not propagate in the vacuum of space as there are

almost no particles present to oscillate and transfer the energy—as made famous by the catchline of the 20th Century Fox film Alien, which was made in 1979: ‘In space, no-one can hear you scream.’ Figure 7.1.4 Something to scream about—

a model of the 6 m alien ‘Queen

Mother’ from the movie Aliens.

Relate compressions and rarefactions of sound waves to the crests and troughs of transverse waves used to represent them.

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A sound wave with a pure, single frequency, such as a wave produced by a tuning fork, can be represented using a simple sine wave (Figure 7.1.5a). However, most sound waves are made up of a mixture of sine waves of different frequencies (called harmonics or overtones), and these waves superimpose to produce a complex wave form. These complex waves are the norm as the sources of most sounds are not ideal. An ideal source is usually symmetrical, has a simple shape and mostly oscillates as a sine wave at a single frequency.

Most sound sources are not ideal as they produce a number of sound waves of different frequencies at the same time. For example, when a person speaks or sings, the folds of tissue that make up the larynx vibrate at many frequencies; however, the surfaces and cavities of the throat, nose and mouth filter out some frequencies, but not others, resulting in the rich mixture of frequencies. All of these sound waves superimpose to give the human voice its distinctive sound (Figure 7.1.5b).

a b

Figure 7.1.5 Wave forms produced by (a) a tuning fork and (b) a human voice humming. The tuning fork can produce a pure, single frequency sound, whereas the human voice produces a number of sound waves of different frequencies at the same time.

Sound waves travel through all media whose particles can be compressed. The speed of sound waves in different media depends on the density and

elasticity of the medium. Table 7.1.1 shows the speed of sound in some common solids, liquids and gases.

Table 7.1.1 Speed of sound in some common substances

SUBSTANCE SPEED OF SOUND (m s –1)Dry air at 0° 331

Dry air at 20° 344

Helium at 0° 965

Water vapour at 134° 494

Distilled water at 25° 1497

Sea water at 25° 1531

Stainless steel 5790 (longitudinal wave in bulk material)

Aluminium 6420 (longitudinal wave in bulk material)

Activity 7.1

PRACTICAL EXPERIENCES

Activity Manual, Page 68


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The difference in the speed of sound in different media is the basis of a number of technologies. For example, the relationship between the temperature of a medium and the speed of sound is used in oceanography to map the temperature variations in bodies of water. Pulses of sound can be transmitted and then detected at long distances. The detection time can be used to determine the temperature of the intervening column of water. Temperature mapping of the world’s oceans is an important tool in predicting the extent of global warming.

PHYSICS FEATURESOUND WAVE SPEED AND EVOLUTION OF EAR STRUCTURES

Sound can propagate quickly and over great distances through water. In comparison, air is a

much poorer conductor of sound waves. This physical property—sound wave speed in water and air—is evident in the evolution of the ear structures of dolphins and humans. Water-based mammals, like dolphins, have highly developed auditory systems, and the auditory nerve that conducts impulses from the ear to the brain has twice as many nerve endings as the auditory nerve of humans. Sound perception is an important survival tool in a marine environment, where sound conduction is high but light levels and visibility are low.

Land mammals, including humans, have had to evolve sound detection systems that maximise sound detection in air. As sound travels more slowly and is dissipated more readily in air, human ears have a number of additional features. The most obvious difference between a human and dolphin ear is the

external ear structure. Humans have developed a shell-like structure of cartilage and skin to collect faint sound waves travelling through the air. An eardrum is also required in humans to amplify the sound waves. Dolphins have no eardrum and no external ears. Sound waves are detected directly through the fatty tissue of the lower jaw.

Figure 7.1.6 Dolphins have no external ear structure.

CHECKPOINT 7.11 A sine wave can be used to mathematically represent a sound wave. There are two possible ways to do this: by

considering either (a) pressure changes over time or (b) particle displacement over time. Choose one option and describe how the compressions and rarefactions of the medium are represented in the sine wave. Include a diagram in your answer.

2 What factors affect the speed of a sound wave through a medium?


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7.2 Pitch and volumeThe solids, liquids and gases that surround us can easily conduct the mechanical vibrations of sound waves for our ears to detect, but how do we make sense of these sound waves? People, including tiny babies, can recognise the voice of a familiar person in a crowd. We have seen that most sounds have a complex waveform and that different sounds look different when displayed on an oscilloscope. This means that each sound has a distinctive pitch, volume and timbre—properties that allow us to distinguish differences in sounds. This section explains pitch, volume and timbre in terms of the wave concepts introduced in Chapters 5 and 6.

A source of sound—such as vocal chords, a guitar string, a speaker diaphragm, a ringing bell or a car motor—produces vibrations that have a frequency and an amplitude. You should recall that frequency is the number of oscillation cycles completed by the source per second, and amplitude is the maximum pressure change imparted to the particles in the medium by the source (Figure 7.2.1).

256 Hz

256 Hz

signalgenerator

signalgenerator

cathode ray oscilloscope (or computer)

a b

Figure 7.2.1 Two audio signal generators are connected to an oscilloscope and both channels are displayed on the screen. (a) The signal generators produce waves of the same frequency but different amplitudes. (b) The signal generators produce waves of the same amplitude but different frequency.

PitchA healthy human ear is capable of detecting sound waves within a frequency range of roughly 20 Hz to 20 kHz. Sound waves of different frequencies stimulate different nerve endings in the snail-like cochlea in the inner ear, and these nerve impulses are conducted to the brain where they are interpreted as sounds of varying pitch. The brain recognises low-frequency sound waves as low-pitch sounds and high-frequency sound waves as high-pitch sounds. In sounds that are a mixture of frequencies, the pitch is determined by the lowest (audible) frequency in the mixture.

Explain qualitatively that pitch is related to frequency and volume to amplitude of sound waves.


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The human ear is extremely sensitive to pitch and can distinguish between sound waves varying in frequency by as little as 1 Hz. Pitch sensitivity, particularly in the 10–20 kHz range, declines as people age or if the ear is damaged. For example, mobile phone ring tones that claim to be inaudible to parents and teachers are typically sound waves of 15 to 17 kHz; most adults (but not all) are unable to detect these high-pitch sounds as nerve endings in their ears have degraded. Some shopping malls in the United States attempted to prevent ‘loitering youth’ by playing these same high-frequency sounds annoyingly loudly in areas where young people liked to congregate.

A physical phenomenon related to frequency is resonance. If you were to take a stiff plastic ruler and hold one end firmly against a tabletop while you flick the other end with your fingers, the ruler would start to vibrate (Figure 7.2.2). The ruler will vibrate at its natural frequency. The physical parameters—such as size, shape and materials—of any object determine its natural frequency. If you reduce the length of ruler overhanging the table edge, you can hear the natural frequency increase. This natural frequency of an object is called the resonant frequency. It is easy to get an object to vibrate at its resonant frequency and hard to get it to vibrate at other frequencies.

PHYSICS FEATUREPERFECT PITCH

If most people are played a note on the piano, they would be able to tell if a subsequent note was

higher or lower in pitch (frequency). Discerning the pitch of a sound given a reference point is called relative pitch perception, and all people with reasonable hearing can do this. Some people, however, can tell you the pitch from hearing only a single note played, or they can sing a note of a stated

pitch without any assistance or prompt. These people (approximately 1 in 2000) have the ability to identify the pitch of a musical tone without the aid of an external pitch reference. This absolute pitch perception ability is known as perfect pitch. The majority of people with perfect pitch have had formal musical training from a young age, but it is unclear if perfect pitch is a learnt skill, a genetic trait or a combination of both.

VolumeThe volume or loudness of a sound is related to the energy of the sound wave. A soft or low-volume sound wave carries less energy than a loud or high-volume sound wave. If you recall, in Section 6.1 we related the energy of waves to the amplitude:

Ewave amplitude2

The volume of a sound depends on the sound wave’s amplitude. A sound wave with given amplitude will create a pressure difference in the particles of the medium. When detected by the ear, this pressure causes the eardrum to bow in and out, transmitting the pressure waves through three small bones to fluid in the cochlea in the inner ear. Pressure waves cause nerves to produce pulses; the greater the pressure, the more pulses produced. The number of pulses reaching the brain is interpreted as loudness.

Figure 7.2.2 A ruler vibrates at its natural or resonant frequency when the overhanging end is flicked.


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TimbreIf two people were to hum, each making a sound of the same pitch and volume, it would still be possible to distinguish between the two sounds. This is due to the quality or timbre (a French word pronounced tamber) of the sounds produced by each person. As described previously, the sound produced by a person humming is not a simple sine wave but a complex waveform that results from superimposing many simple waves. Timbre refers to the sensation you get by detecting the different frequencies of the component waves in the sound. Each person produces a slightly different combination of sound waves of varying frequency, which gives each voice its distinguishing characteristics. Timbre is the property that allows a baby to recognise its mother’s voice, you to recognise a friend’s voice on the phone or a musician to choose between two different violins.

a tuning fork b clarinet c cornet

Figure 7.2.3 The waveform of a sound can be displayed using an oscilloscope. These three waveforms produced by (a) a tuning fork, (b) a clarinet and (c) a cornet all have the same frequency and amplitude. All three sounds look and would sound different. This is because of timbre.

CHECKPOINT 7.21 Define the terms pitch, volume and timbre as they apply to

sound waves.2 Compare the pitch and volume of the two sound waves shown in

Figure 7.2.4.

Figure 7.2.4


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7.3 Reflection of sound wavesEchoIf you stand at a mountain lookout on a still day and call out in a loud voice, you will hear your voice repeated back to you. This is an echo. The echo phenomenon is caused by the sound waves you generate being reflected back towards you by the rock surfaces of the mountains. There will be a delay before you hear the echo as the sound waves have to travel to and from the reflective surface. Any large reflective space, such as a hall or empty room, is capable of producing an echo as long as the delay between the original and reflected sounds is at least 50 ms because the human brain tends to treat sounds closer together than 50 ms as a single sound.

An echo is heard most clearly when the majority of the sound wave energy is reflected at the boundary, rather than being absorbed or transmitted by the new medium. The reflected sound wave will superimpose with the original wave, causing a blending of sounds. To perceive a clear echo, a series of short sharp sounds are better than a long continuous one because short sound pulses are less likely to interfere with the reflected sound wave.

Figure 7.3.1 On still mornings you can make an impressive echo at Echo Point at Katoomba, NSW. Sound waves are reflected from the rock formation known as the Three Sisters.

ReverberationIn a room with smooth, hard walls, echoes can travel back and forth many times. If a large number of echoes reach the human ear in a short period of time, we are unable to distinguish between them and the sound seems to smear out, lasting a long time. This effect is called reverberation. Some quiet reverberation is important for both musicians and audiences. It gives a performance venue a feeling of spaciousness, helps the quieter instruments like strings and woodwind to be heard, and allows the sounds from a range of instruments and voices to blend in a pleasing way.

Explain an echo as a reflection of a sound wave.


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Concert halls and venues have characteristic reverberation times—the time needed for a sound wave intensity to decrease to 0.001 of its original amplitude. Venues designed for acoustic music and singing typically have reverberation times between 1 and 2 s. For example, the Sydney Opera House Opera Theatre has a reverberation time of 1.4 s. A hall designed for public speaking has a shorter reverberation time (typically 0.7 to 1 s) so that the words heard by the audience are clear and distinct. In a room with longer reverberation time, speech can sound muffled or blurred and be therefore difficult to understand; in these situations, amplification of the speaker’s voice is usually required. A room with no reverberation feels dead and a room with loud reverberation feels noisy.

The reverberation characteristics of a room can be changed by using sound-absorbing materials on the room surfaces, such as curtains, carpets and egg carton-like wall lining. The size and shape of a room also contributes to reverberation.

Worked exampleQUESTIONSuppose you were to stand at one end of an empty room and make a loud noise. If we take the speed of sound in air to be 340 m s–1, what is the shortest possible length of the room for you to be able to hear an echo?

SOLUTIONThe time difference between the reflected sound and the original noise would have to be at least 50 ms. The sound pulse will travel from one end of the room to the other and back (twice the room length) in 50 ms.

Speed = distance

timeRearrange: Distance = speed × time = 340 m s–1 × 50 × 10–3 s = 17 m

Find the room length: Room length = distance

2 = 8.5 m (to 2 significant figures)

EcholocationEcholocation is a technique that uses echoes (or reflected sound waves) to determine the distance to an object. Bats are animals that have evolved a sense of hearing so sophisticated that they can easily navigate and capture small flying insects in the dark. A flying bat emits short high-frequency sound pulses up to 200 times per second. These sound pulses bounce off insects, cave walls and other objects and are detected by extremely sensitive acoustic receptors inside the bat’s ears.

Humans have used electronic transducers and computers to mimic the bat’s technique with technologies such as SONAR (SOund Navigation And Ranging) and medical ultrasound. SONAR is primarily used to navigate and locate ocean-going vessels; it is also used to locate fish and survey features on the ocean floor (Figure 7.3.2). Depending on the application, SONAR can use infrasonic (lower than 20 Hz) or ultrasonic (higher than 20 kHz) frequencies of sound. Medical ultrasound is a non-invasive diagnostic technique used to view the internal structures of the body. High-frequency sound pulses are emitted into the body where they reflect from boundaries between different media, such as muscle, bone and water.


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Figure 7.3.2 SONAR image of three underwater volcanoes known as the Three Wise Men. The colours correspond to depth: from blue (deepest) through green, yellow and red to white (shallowest).

Worked exampleQUESTIONA SONAR-based fish finder detects a school of fish 2.81 m below the fishing boat. If the fish finder detects an echo time difference of 3.85 ms, what is the speed of sound in the water below the boat?

SOLUTIONThe sound pulse travels from the boat to the fish and back. The sound pulse travels (2.81 × 2) m in 3.85 ms.

Speed = distance

time

= ( . )2 81 2

3

×× −

m3.85 10 s

= 1459.7 m s–1

The speed of sound in the water beneath the boat is 1460 m s–1 (to 3 significant figures).

CHECKPOINT 7.31 What is the difference between an echo and a reverberation?2 Describe a technology that utilises the physics of sound reflection.


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7.4 Superposition of sound wavesSound waves superimpose (or interfere) in the same way as any other wave. The resultant wave depends on the frequency, amplitude and phase of the component waves. Under the right conditions, it is possible for sound waves to constructively and destructively interfere, as described in Section 6.4. Let us consider an example as illustrated by Figure 7.4.1.

Constructive and destructive interferenceSuppose we have two identical and ideal sound sources (S1 and S2) that are emitting sounds of the same frequency and the same phase. If we wish to determine the superimposed waveform at point P some distance from the sources, we could draw two rays: one from each source to point P. If the sound waves travelled along these paths, they would travel a distance of L1 and L2 from sources S1 and S2 respectively. If the distances L1 and L2 are the same, the two waves arrive at point P with the same phase and constructively interfere. At points of constructive interference, the amplitude of the sound wave would double and the volume would increase. If the distances L1 and L2 are different, however, the waves may not be in phase at point P. The difference between L1 and L2 (ΔL) is called the path length difference. If the path length difference is equal to 0, λ, 2λ, 3λ, 4λ or any integer multiple of the wavelength, the two waves will be in phase and constructively interfere. Destructive interference will occur when the two waves are 180° out of phase or half a wavelength out of step.

This corresponds to ΔL = λ2

, 32λ

, 52λ

and so on. At these points, the

amplitude and volume of the sound would be zero.

Describe the principle of superposition and compare the resulting waves to the original waves in sound.

S1L1

L2

P

S2

Figure 7.4.1 Two identical sound waves are emitted from sources S1 and S2, as shown by the rays. The waves travel distances L1 and L2 to point P.

TRY THIS!HEARING INTERFERENCEUse a signal generator to produce a sound of a single frequency and connect to two speakers at least 1 or 2 m apart. Walk slowly along a straight line in front of the two speakers. You should be able to clearly detect the regions of constructive and destructive interference by listening for the change in volume.

soft

soft

soft

soft

loud

loud

loud

Figure 7.4.2 As you walk, you should hear alternating loud and soft sound coming from the speakers. The wave fronts from each speaker are shown in two different colours, orange and blue. Constructive interference occurs where the wave fronts overlap; you will hear a louder sound at this point.


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Standing waves In special circumstances, sound waves will superimpose (or combine) to

produce a steady-state distribution of energy known as a standing wave or stationary wave. Unlike other waves, standing waves don’t travel; instead, a pattern forms with regions of zero oscillation (nodes) and maximum oscillation (anti-nodes) both fixed in space.

Standing waves occur in the throat and head when we speak or sing, and are produced by every type of musical instrument from drums and guitars to pianos and tubas. Standing waves are also produced when a sound wave interferes with its own reflection. In this case, we have two waves with the same amplitude and frequency travelling in opposite directions. Figure 7.4.3 shows the two waves and the resultant superimposed wave at different points in time.

As they combine, a fixed pattern of nodes and anti-nodes is established. At a node the resultant displacement is zero; at an anti-node, the displacement oscillates between a maximum positive value and a maximum negative value. The distance between two nodes is half a wavelength (Figure 7.4.4). Standing waves are established between boundaries; these boundaries can be fixed or free, as described in Section 6.4.

t = 0 s anti-node

node

node node

node

anti-node anti-node

t = 1.5 s

t = 3 s

t = 4.5 s

t = 6 s

anti-node

node

node node

node

anti-node anti-node

a

b

c

Figure 7.4.4 This illustrates the standing wave only, not the component waves that superimpose (which is shown in Figure 7.4.3). (a) A standing wave between two fixed ends is illustrated at five different points in time. (b) All of the five illustrations from (a) on one diagram. The nodes and anti-nodes are labelled. You can see that the distance between two nodes is half a wavelength. (c) A common and widely used physics representation of the standing wave from (a).

Let us consider an example of a standing wave produced between two fixed boundaries, such as a clamped string on a guitar. If the string was oscillated at natural or resonant frequencies, a standing wave with nodes and large anti-nodes would be produced. If the string was forced to oscillate at another non-resonant frequency, no standing wave would be produced and only tiny vibrations of the string would be observed. The resonant frequencies of a string depend on the distance between the clamped ends. There are many possible patterns of nodes and anti-nodes for a guitar string. A node must exist at each clamped end as

t = 0 s

t = 1 s

t = 3 s

t = 4 s

t = 5 s

t = 6 s

t = 7 s

Figure 7.4.3 This diagram shows two identical waves travelling in opposite directions (coloured green and red). The green wave appears slightly smaller so that it is clearly visible on the diagram. These two waves superimpose to produce the stationary wave shown in blue. At t = 0 s, the stationary wave is at maximum displacement; at t = 4 s, the stationary wave has zero displacement.


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these are fixed boundaries and cannot oscillate. Along the length of the string there could be any number of nodes and anti-nodes. The first three possible patterns are shown in Figure 7.4.5.

L

L = λ

n = 1

n = 2

n = 3

L = λ

L = 3λ2

2

Figure 7.4.5 The first three simplest patterns of standing waves possible in a guitar string. The ends of the string are fixed and will always be nodes.

For the first pattern where one anti-node is present, if the length of the string

is L metres, then λ2 = L as the distance between two nodes is half a wavelength.

This gives us λ = 2L. For the second pattern, two anti-nodes are present and a complete wavelength occurs between the two fixed ends, so λ = L. In the final pattern, one and a half wavelengths occur between the two fixed ends, so 32λ = L or λ = 2

3L. If we continue this pattern, we would set up standing

waves on a string of length L metres by waves with wavelengths given by:

λ = 2Ln

, for n = 1, 2, 3, 4, 5…

Using the wave speed equation v = f λ, we can determine the resonant frequencies that correspond to these wavelengths:

fv

nvL

= =λ 2

, for n = 1, 2, 3, 4, 5 …

The lowest resonant frequency that corresponds to the first pattern with one anti-node is called the fundamental frequency or first harmonic. The second harmonic is the oscillation mode with n = 2, the third harmonic is n = 3 and so on. The collection of all possible oscillation modes is called the harmonic series. An oscillating system with two fixed ends can therefore be used to describe guitars, violins, violas, cellos, double basses, pianos and drums (Figure 7.4.6).


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Figure 7.4.6 Standing wave pattern (third harmonic) produced on a string made to oscillate by a vibrator at the right end. The left end is fixed using a weight.

Other oscillation systems with different boundary conditions are possible. For example, pipes are oscillating systems with either two open ends or one open end. (As discussed in Section 7.1, we can consider either displacement or pressure when discussing sound waves in air. For sound waves, an anti-node of displacement is a node of pressure and vice versa. For this discussion, it is simplest if we only consider displacement.)

The open end of a pipe corresponds to a free boundary because particles are mostly free to displace at an open end, so an anti-node of displacement must be present at an open end. However, if one end of a pipe is closed, particles nearest the closed end are not free to displace through the boundary, so a closed end is a fixed boundary and must correspond with a node of displacement.

Musical instruments based on pipes or columns of air include trumpets, tubas, clarinets, oboes, saxophones, didgeridoos and organs. The first three harmonics for pipes are shown in Figure 7.4.7.

a Pipe with both ends open b Pipe with one end (the left) closed

L

λ =

λ = L

n = 1

n = 2

n = 3

λ = L

2

L

λ = 4L

λ = 4L

3

λ = 4L

52L3

Figure 7.4.7 Standing wave patterns produced by pipes. (a) The first three harmonics of an open-ended pipe: the open ends correspond to free boundaries, so they will be displacement anti-nodes. (b) The first three harmonics of a closed pipe. The left end is a fixed boundary and a node.

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The resonant frequencies for a pipe with two open ends can be calculated using this equation:

fv

nvL

= =λ 2

for n = 1, 2, 3, 4, 5 …

The resonant frequencies for a pipe with one open end can be calculated using this equation:

fv

nvL

= =λ 4

for n = 1, 3, 5, 7 …

Worked exampleQUESTIONThe water level in a large measuring cylinder 50 cm long can be adjusted to any level in the cylinder. A tuning fork vibrating at 480 Hz is held just over the open end of the measuring cylinder to set up a standing soundwave in the air-filled portion of the cylinder. Assuming the speed of sound in air is 348 m s–1, at what positions of the water level is there resonance?

SOLUTIONThe air-filled portion of the measuring cylinder acts as an open pipe. The water is the fixed boundary and the other boundary is free.

Resonant frequencies are given by the equation: f = nvL4

for n = 1, 3, 5, 7 …

Rearrange the equation for L the length of the air cylinder: L nvf

=4

for n = 1, 3, 5, 7…

Take n = 1.

L = ××

1348

4 480 = 0.18 m of air, which corresponds to a water level of (0.5 – 0.18) m = 32 cm.

Take n = 3.

L = ××

3348

4 480 = 0.54 m of air, which is larger than the space available in a 50 cm

measuring cylinder.

Resonance will occur at a water level of 32 cm.

STANDING IN THE MICROWAVE?

When operating, a microwave oven is full of standing

electromagnetic waves. Therefore there are nodes (low intensity) and anti-nodes (high intensity), which means there will be hot and cold spots respectively. To prevent uneven cooking, the turntable inside rotates the food to smooth out any variation.

Present graphical information, solve problems and analyse information involving superposition of sound waves.

Activity 7.2

PRACTICAL EXPERIENCES

Activity Manual, Page 74

CHECKPOINT 7.41 Complete the following table to show the relationship between phase and path length difference.

PHASE DIFFERENCE (DEGREES) PHASE DIFFERENCE (RADIANS) PATH LENGTH DIFFERENCE (METRES) 0

λ4

π

270

2π

2 Describe the displacement of particles in a medium relative to the equilibrium at a node and an anti-node.

PRACTICAL EXPERIENCESTHE WORLDCOMMUNICATES

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CHAPTER 7This is a starting point to get you thinking about the mandatory practical experiences outlined in the syllabus. For detailed instructions and advice, use in2 Physics @ Preliminary Activity Manual.

ACTIVITY 7.1: OBSERVING AND ANALYSING SOUND WAVESUse an audio microphone connected to an oscilloscope to observe and analyse the waveforms produced by various sources of sound waves, including the human voice, tuning forks and musical instruments.Equipment list: oscilloscope, audio microphone, signal generator, tuning forks, musical instruments, human voice, graph paper.

cathode ray oscilloscope (or computer)

Figure 7.5.1 An audio microphone is connected to an oscilloscope.

Discussion questions1 Compare the waveforms produced by two people making the sound

‘eeeeeeeeeeee’.2 Compare the waveforms produced by one person making the sounds

‘aaaaaaah’, ‘eeeeeee’ and all the other vowels.3 Explain why the tuning forks produce sine waves while other sources

produce more complex waveforms.

ACTIVITY 7.2: MEASURING THE SPEED OF SOUNDUse the equipment listed and the theory of standing waves to design an experiment to calculate the speed of sound in air.Equipment list: large measuring cylinder or glass tube with rubber stopper, tuning forks, ruler, water.

Discussion questions1 Explain how temperature and humidity

affect the speed of sound in air.2 How could you improve the accuracy

and validity of your results in this experiment?

Perform a first-hand investigation and gather information to analyse sound waves from a variety of sources using the cathode ray oscilloscope (CRO) or an alternative computer technology.

Plan, choose equipment for and perform a first-hand investigation to gather information to identify the relationship between the frequency and wavelength of a sound wave travelling at a constant velocity.

Figure 7.5.2 Experimental equipment used to measure the speed of sound

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Chapter summary• Sound is a mechanical wave caused by a vibrating source.• Sound waves require a medium to propagate.• Sound waves are longitudinal waves.• A sine wave can be used to represent a sound wave

mathematically. The maximum and minimum points of the sine wave can correspond to either maximum and minimum pressure of the air particles, or maximum and minimum displacement of the air particles from an equilibrium position.

• Sound waves of a single frequency are produced by ideal (symmetrical) sources and can be mathematically represented by a sine wave.

• Most sound waves are made up of a number of sine waves of different frequencies. These waves superimpose to produce a complex waveform.

• The speed of sound through a medium depends on the medium’s density and elasticity.

• Different sound waves have different pitch, volume and timbre.

• Low-pitch sounds have a low frequency; high-pitch sounds have a high frequency.

• The volume of a sound wave is related to the energy of the sound wave.

• Ewave amplitude2

• A soft or low-volume sound corresponds to a small amplitude; a loud or high-volume sound corresponds to a large amplitude.

• The timbre of a sound wave is determined by the combination of frequencies that make up a complex waveform.

• An echo is a repetition of a sound caused by the reflection of the original sound wave.

• Two sound waves (initially in phase) will constructively interfere if the path length difference is any integer multiple of the wavelength (ΔL = 0, λ, 2λ, 3λ, 4λ).

• Two sound waves (initially in phase) will destructively interfere if the path length difference is:

Δ L = λ2

, 32λ

, 52λ

• In special circumstances, sound waves will superimpose to produce standing waves.

• Standing waves consist of nodes and anti-nodes. The net displacement at a node is zero; the displacement at an anti-node oscillates between minimum and maximum displacement.

• The distance between two nodes is half a wavelength.• Standing waves are only produced at certain frequencies

called resonant frequencies.

PHYSICALLY SPEAKING1 Rate your knowledge on the key concepts in this chapter by completing the table below. Tick the box that most accurately

describes your present knowledge—be honest.

CONCEPT GOOD UNDERSTANDING(very confident, could give a definition and examples for this concept)

PARTIAL UNDERSTANDING(have heard of this concept, could give an example or partial definition)

NONE(never heard of this before or am very confused by this concept)

Longitudinal waves

Speed of sound

Pitch

Volume

Echo

Superposition of soundwaves

Review questions

2 Share your knowledge rating with another student, pool your knowledge and complete a brainstorm summary chart on blank paper, like the one shown below. Where you have any gaps in your knowledge, reread the textbook or ask your teacher. Fill in any gaps in the table using a different coloured pen. This will assist you when revising for tests or assessments.

CONCEPT DEFINITION EXAMPLES DIAGRAMS/EQUATIONSLongitudinal waves • Vibrates same direction as wave

travels• Compression• Rarefaction

• Sound wave• Slinky wave

compression


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REVIEWING 1 An astronaut soldering electronics to the outside of the International Space

Station would be able to see an exploding gas cylinder but would not hear the explosion. Explain why this is the case.

2 A tourist standing at Echo Point, Katoomba, can see the rocky outcrop called the Three Sisters approximately 500 m away. If the tourist was to call out ‘Hello’ in a loud voice, they would hear their greeting repeated back to them 2.9 s later.a Explain why the tourist would hear a repeated ‘Hello’.b Calculate the speed of sound at Echo Point for this example.

3 The human brain can only detect an echo if the delay between the original and reflected sound is greater than 50 ms. A scuba diver is helping to assemble an offshore oil rig. What is the minimum distance between the diver and the supply ship for the diver to hear an echo from the supply ship hull? Assume the speed of sound in the sea water is 1500 m s–1.

4 An ultrasonic sound wave measures the distance to a bone from the skin surface to be 1.6 cm. The speed of sound through muscle and fat is approximately 1480 m s–1. Calculate the time delay detected by the ultrasound receiver that corresponds to this bone distance.

5 In some workplaces, loud and repetitive machinery noise can permanently damage the hearing of employees. Special headphones are worn by the employees that replay a copy of the machinery noise. The employees say the headphones help cancel out the noise. Explain how this technology works in terms of the superposition of sound waves.

6 Humans can hear sound waves in the range 20 Hz to 20 kHz, while bats operate in the higher frequency range 1 kHz to 150 kHz. Compare the wavelength of sound waves detected by humans and bats, assuming the speed of sound is 344 m s–1.

7 An audio signal generator produces a trace on an oscilloscope, as shown in Figure 7.5.3. The horizontal scale is set to 5 ms per division. Determine the period and the frequency of the sound wave.

8 Spectators watching the New Year’s Eve fireworks on Sydney Harbour notice a delay between seeing the colourful explosion and hearing it.a Explain why this occurs.b Compare the sound delay for two spectators watching the fireworks

on the Sydney Harbour Bridge. One spectator is standing 200 m away at Milsons Point; the other is standing 1.2 km away at Mrs Macquarie’s Chair.

9 Two students attempt to measure the speed of sound using an athletics starting pistol and a stopwatch. One student stands at one end of the school oval and fires the starting pistol. The second student stands 500 m away at the other end of the oval. She starts the stopwatch when she sees the smoke from the pistol and stops the stopwatch when she hears the loud cracking sound. She records the following six times: 1.40 s, 1.52 s, 1.48 s, 1.37 s, 1.45 s and 1.54 s.a Record the data in an appropriate table.b Calculate the average time from the data.c Calculate the speed of sound for this experiment.d What is the benefit of recording six times in this experiment?e Identify two possible sources of error in this experiment.

Figure 7.5.3 The horizontal scale of the oscilloscope is 5 ms per division.

7 Hear thedifference: soundHeHeHeHeHeararararar t t t t thehehehehedididididifffffffffferererererenenenenencecececece: : : : : sosososos unununununddddd

134

10 The speed of sound in helium gas at 0°C is 965 m s–1 compared with 330 m s–1 for air under the same conditions. If you inhale a little helium and speak while exhaling, your voice will sound squeaky. Can you account for the difference in the sound of your voice? Note: Inhaling helium displaces the oxygen in your respiratory system and can be extremely dangerous. Possible side effects include lung tissue damage, blackouts and stroke from helium bubbles in the bloodstream.

SOLVING PROBLEMS 11 The speed of sound at sea level when the air is dry and the temperature is

0°C is 330 m s–1. For the usual range of temperatures encountered at sea level, the speed of sound increases by 0.60 m s–1 for each increase of 1.0°C.a Describe what happens to the speed of sound at the beach as the Sun

rises and warms the atmosphere.b At what temperature will the speed of sound equal 320 m s–1?

12 A thin wire is stretched between two pegs 40 cm apart. The wire is bowed and set into oscillation.a Sketch the patterns produced by the fundamental and the second

harmonic. Label your diagrams showing lengths, nodes and anti-nodes.b Calculate the wavelengths of the fundamental and second harmonic.

13 Sara fills a test tube with 4 cm of water, leaving two-thirds of the tube empty. She gently blows over the end of the test tube, producing a low-pitch sound. She repeats the process, this time adding water until the tube is three-quarters full and producing a high-pitch sound.a Sketch the patterns produced by the fundamental frequency for both

sounds. Label your diagrams showing lengths, nodes and anti-nodes.b Calculate the wavelength of the fundamental in both cases.

14 A B string on a guitar is held fixed at both ends under tension with a vibrating length of 33 cm. Once plucked, it oscillates at a fundamental frequency of 246 Hz. What are the wavelengths on the string and in the air at 20°C?

15 An organ pipe that ordinarily sounds with a fundamental frequency of 800 Hz at 0°C is connected to a source of helium at that temperature. What is the fundamental frequency of the helium-filled organ pipe?

EXTENSION 16 Imagine a hypothetical piano with all strings made of the same material

and under the same tension and hence the same sound velocity within all strings. The piano has a frequency range of 27.7 Hz to 4186 Hz (7 octaves); the highest note is produced by a string 15 cm long. a What string length is required to produce the lowest note?b Why is this poor design for a piano?

Present graphical information, solve problems and analyse information involving superposition of sound waves.


135

PHYSICS FOCUSCONCERT SOUND

Figure 7.5.4 The sweet sound of Kylie in concert

What was the last concert that you went to? You will remember hearing the singer’s voice and the music, but did you give any thought to how the sound travelled? Probably not as you were enjoying yourself too much! Apply your knowledge of waves from this chapter to answer the following questions about sound at a concert.

1 Outline an example of a one-, two- and three-dimensional wave that you could experience at a concert.

2 Define the term medium and give an example relating to waves at a concert.

3 Describe the properties of sound waves and how they travel. In your answer, use a diagram to demonstrate the structure of a sound wave, including the wavelength, period and amplitude.

4 You may remember hearing various sounds—high pitch and low pitch, loud and soft—at a concert. Explain how pitch and loudness are related to the structure of a sound wave.

5 Many concerts are broadcast via satellite to other parts of the world. Identify the types of waves used to transfer the music or information via satellite.

6 Compare the sound waves that carry the music from the speakers to your ears with those used to transfer the same music via satellite.

7 As sound waves travel from the speakers in a concert hall, sometimes you may hear the sound a second time after it has initially reached your ears. Explain this phenomenon and how it may occur.

8 Describe the features of a concert hall that are designed to maintain high-quality sound and to stop the phenomenon you described in Question 7 from becoming a problem.

9 A typical band includes drums, which are used to provide the rhythm or beat for the music. A drum consists of a hollow cylinder with a tight skin covering one end. A large kick (or base) drum produces a lower frequency sound than the small snare drum. Discuss the relevance of shape and size of the drum to the sound it produces.

EXTENSION10 The use of low-frequency SONAR in the world’s

oceans for oil exploration and defence purposes has been blamed for the change of behaviour in migrating whales hundreds of kilometers away. A spokesman from the Whale and Dolphin Conservation Society said: ‘Flight, avoidance or other changes in behaviour have been observed in cetaceans (whales or dolphins) from tens to hundreds of kilometres from the noise sources. It has even been suggested that the abilities of the great whales to communicate with each other across entire ocean basins has now been reduced by orders of magnitude.’ Evaluate this statement.

11 In the 1950 Superman movie Atom Man vs. Superman, Superman is told to stop trying to save Lois; otherwise Lex Luthor would continue causing earthquakes with his sonic beam. Is this a plausible plot?

4. Describe applications of physics which affect society or the environment

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