Sound Waves: Characteristics and Applications: Class 9 Science · Chapter 10

A pressure cooker whistles in the kitchen, an auto-rickshaw honks outside, a temple bell rings down the lane and a friend calls your name from the next room. You know what each of these is without looking, because each one reaches you as sound.

In Chapter 7 you saw that energy never appears from nothing or disappears; it only changes form. Sound is one of those forms. This chapter asks three questions. What kind of motion makes a sound? How does that sound get from its source to your ear? And what can we measure about it? The answers explain echoes in a hall, the shrill note of a referee's whistle and how a ship finds a wreck far below the waves.

10.1 Production of Sound

Twang a steel ruler pressed on the edge of a desk, tap a steel glass with a spoon, or blow across the mouth of an empty bottle. Each time something shakes rapidly back and forth, and you hear a sound. You have made sounds like these in your arts classes. In Grade 7 you also met sonority: the ringing sound that metals such as brass and steel give when they are struck, as a temple bell or a pair of manjira does.

So sound is produced by a vibrating object, and the object that vibrates is called the source of the sound. Sources come in a few families: stretched strings (sitar, ektara), stretched skins or membranes (tabla, dholak), columns of air (bansuri, shehnai, conch) and solid bodies (bell, manjira). Most instruments use more than one. In a sitar, the strings shake the hollow gourd, and the air inside the gourd vibrates too.

Rest your fingertips lightly on the front of your throat and hum: you feel a buzz. It comes from the vocal cords, two folds of muscle stretched across your voice box (the larynx). Breath pushed up from the lungs sets them vibrating as they open and close. Your tongue, teeth, lips and the hollows of your mouth and nose then mould that buzz into words or a song. Insects have other tricks: a cicada clicks drum-like plates on its body, and a cricket scrapes a ridged edge of one wing over the other.

10.1.1 Tuning fork

Music teachers and physics labs keep the same handy sound source: the tuning fork. Picture a capital U of steel or aluminium standing on a short handle, the stem. Tap one of its two arms, the prongs (or tines), on a rubber pad and the fork rings with one steady, clean note. Each fork always gives the same note, and its value is stamped on it.

10.2 Propagation of Sound

A sound has to cross the gap between its source and you. Air is the obvious route. But can sound also pass through a wooden bench, or through a bucket of water? Two quick tests settle it.

Wood, water, air: sound got through all three. The stuff a sound passes through on its way to you is its medium, which can be any state of matter: solid, liquid or gas.

That raises a puzzle. What if there were no stuff at all between the source and you? A region empty of all matter is a vacuum. Can sound cross one?

10.2.1 Sound needs a medium to propagate

Put a battery buzzer under an airtight glass dome, a bell jar, standing on a plate that is connected to a vacuum pump. Switch on the buzzer: you hear it clearly. Now start pumping out the air Fig. 10.3.

The loudness bar in Fig. 10.3 tells the story. The fewer air particles left in the jar, the fainter the ring, yet through the glass you can see the hammer striking the whole time. With hardly any air left, the buzzer is close to silent; open the valve and the ringing comes back. The buzzer kept vibrating throughout. Only the medium changed, so sound needs a medium, and a vacuum does not carry it.

Space between the planets is almost a perfect vacuum. A spanner clanging against a satellite sends no sound through empty space to an astronaut floating nearby. An astronaut touching the satellite, though, could feel the vibration through the metal and the suit. Spacewalkers talk by radio sets inside their helmets: radio waves, like light, need no medium. The same goes for the opening puzzle: the Moon has almost no air, so a clap there sends no sound to a partner five metres away.

10.3 Sound Waves

We know that sound needs a medium. But what actually happens to the air between a drum and your ear? Sound leaves a source in many directions at once (that is why the tuning fork could be heard from every side). The exact pattern depends on the shape of the source. Following all of that is messy, so we simplify, as scientists often do: imagine the sound trapped in a long, narrow pipe, where it can travel only one way.

Now swap the slinky for air in a long tube. One end of the tube is closed by a piston that can slide in and out; the other end is open. The piston is our model of a source: think of it as a loudspeaker cone seen from the side. Follow the steps in Fig. 10.4.

Think of the air in the tube as a long queue of people, each standing one step from the next. At rest every gap is the same, and the air has its normal, average density. Now the piston lurches forward. The first layer of air is shoved into the second before the second has had time to move, so for a moment these particles are packed closer than usual. A packed region like this is a compression (C). The second layer then shoves the third, and the third shoves the fourth. The packed region is passed down the tube like a jolt passing down a queue, while each person only stumbles forward a little and steps back.

When the piston draws back, it leaves a little extra room behind it. The nearest layer of air drifts back into that room, and then the next layer follows. So a region with wider gaps than usual, a rarefaction (R), also runs down the tube.

Keep the piston moving in and out and it launches packed and stretched regions one after the other: C, R, C, R. This travelling pattern of high and low density is a sound wave. Notice what does not travel: the air itself. Only the pattern moves, and the direction in which it moves is the direction of propagation of the wave.

Out in the open, nothing hems the particles in. Each compression pushes outwards on every side and grows into an expanding shell around the source, like a balloon being blown up. A small source therefore sends out spherical shells of compression and rarefaction. When these shells reach your ear, you hear the sound.

Look again at Fig. 10.4. Each particle moves to and fro along the tube, the same line along which the wave travels.

Because sound needs particles to pass the disturbance along, it cannot exist without matter. Waves of this kind are called mechanical waves.

Mechanical waves come in two kinds. Tie one end of a rope to a pole and flick the other end up and down. Humps run along the rope, while each bit of rope moves up and down, at right angles to the direction the humps travel. A wave in which the particles vibrate perpendicular to the direction of travel is a transverse wave Fig. 10.5. Sound, as we have seen, is a longitudinal wave.

10.4 Energy of Sound Waves

A vibrating source does work on the layer of air next to it. Each particle passes the push on by colliding with its neighbours, so energy is handed along from particle to particle, although no particle makes the journey itself. In a sound wave it is energy that travels, not the medium. 11Air particles are never truly still: they dart about at random because of their thermal energy. A passing sound wave adds a small, orderly to-and-fro motion on top of this random motion, and the extra motion fades once the wave has gone by.

10.5 Graphical Representation of a Sound Wave

Freeze a sound wave at one instant and measure the density of the air at points along its path. In the compressions the density is above average; in the rarefactions it is below. Plot density up the page against distance from the source across the page, and you get a smooth, wavy curve. A dashed horizontal line marks the average density, the density of undisturbed air Fig. 10.7.

The peaks of the curve, where the density is greatest, are called crests; they lie at the centres of the compressions. The dips, where the density is least, are called troughs; they lie at the centres of the rarefactions. Between a crest and a trough the density passes through its average value.

A second kind of graph is just as useful. Stand at one fixed point and record the density there as time passes. As compressions and rarefactions sweep by, the density at that point rises and falls, so a graph of density against time has the same wavy shape. Only the label on the horizontal axis changes.

10.6 Characteristics of a Sound Wave

To compare one sound with another, we need quantities we can measure. A sound wave is described by its wavelength, its frequency (and the closely linked time period), its amplitude and its speed.

10.6.1 Wavelength, frequency and time period

The distance from one crest to the next crest, or from one trough to the next trough, is the wavelength of the wave Fig. 10.8. It is written $\lambda$ (the Greek letter lambda). Since it is a length, its SI unit is the metre (m).

Now imagine a tiny density meter fixed at one spot in the air, like a tide gauge on a pier. As the wave goes by, its reading climbs to a high (a compression is passing), sinks to a low (a rarefaction) and climbs again. Each full cycle of the reading, high to low and back to high, is one oscillation. Count the cycles the meter shows in one second and you have the frequency of the wave, written $\nu$ (the Greek letter nu). Its unit, "per second" (${\mathrm{s}}^{-1}$), is called the hertz (Hz).

How long one cycle of the meter reading lasts is the time period $T,$ measured in seconds. If the meter completes 100 cycles every second, each cycle must last one-hundredth of a second. So frequency and time period are reciprocals of each other: the higher the frequency, the shorter the time period.

Most everyday sounds, such as voices, traffic or a pressure cooker, are a mixture of many frequencies at once. A struck tuning fork or a steady whistle comes very close to a single frequency, which is why they are handy for experiments.

10.6.2 Amplitude and intensity of the sound waves

Two sounds can have the same wavelength and frequency and yet differ in how hard they squeeze the air. The greatest amount by which the density moves away from its average value is the amplitude of the wave. On the graph, it is the height of a crest above the dashed average line, or the depth of a trough below it Fig. 10.9.

The bigger the amplitude, the more energy the wave carries. Your grain drum showed this: a hard strike on the plate sent the grains flying much higher than a gentle tap, because far more energy reached the film.

How strongly a sound arrives at a place is measured by its intensity. This is the sound energy that passes each second through one square metre of area held face-on to the direction the sound is travelling.

As sound moves away from a small source, the same energy is spread over larger and larger spherical shells. At twice the distance it is shared over four times the area, and at three times the distance over nine times the area Fig. 10.10. So the intensity falls quickly as you move away, which is why a shout fades as you walk off. It is also why a big temple bell can be heard across the village while a tinkling anklet is lost within a few metres. The bell starts with far more energy to spread.

10.6.3 Speed of Sound

The speed of sound tells us how fast the pattern of compressions and rarefactions moves through the medium. Pick one feature of the wave, say a crest, and ask how far it moves in one second.

Sound moves at different speeds in different media. It is quickest in solids, a little slower in liquids, and slowest of all in gases. It travels roughly four to five times faster in water than in air, and fifteen to twenty times faster in many solids Table 10.4.

Air on a hot, sticky afternoon carries sound a little faster than air on a cold, dry morning: both warmth and moisture raise the speed. In dry air, sound travels at about $331\mathrm{m}\mathrm{/}\mathrm{s}$ at 0 °C and about $346\mathrm{m}\mathrm{/}\mathrm{s}$ at 25 °C, roughly $0.6\mathrm{m}\mathrm{/}\mathrm{s}$ more for every degree.

The low notes and high notes of a song reach you together, so in air every frequency must travel at the same speed. What changes with frequency is the wavelength: $\lambda =v\mathrm{/}\nu ,$ so doubling the frequency halves the wavelength. Try it in Fig. 10.11: raise the frequency and watch the wavelength shrink while the speed stays at $340\mathrm{m}\mathrm{/}\mathrm{s}$ all along. Some porous foams and specially engineered materials break this rule, but air, water and ordinary solids do not.

10.6.4 Human perception of sound

A sound meter and your ear do different jobs. The meter reports numbers (frequency, amplitude, speed) that come out the same whoever reads them. Your ear and brain report experiences: shrill or deep, loud or soft, flute or voice. Pitch and loudness are names for these experiences, and they are tied to the physical numbers only loosely, not by a neat formula Table 10.5.

Pitch is our sense of how high or low a sound is. A mosquito's whine and a pressure-cooker whistle sit high; a bull's bellow and a big dhol sit low. Raising the frequency raises the pitch, but the ear does not measure frequency like a ruler. To your ear, going from 100 Hz to 200 Hz sounds like the same step up as going from 1000 Hz to 2000 Hz.

You know a friend's voice on the phone partly from its frequency. The shape of their throat, mouth and nose matters too, acting like the body of an instrument. In the early teens a boy's voice "breaks": his vocal cords grow longer and heavier, vibrate fewer times each second, and his voice drops lower.

Our ears are deaf to most of the frequencies that exist. A healthy young ear responds only from about 20 Hz to about 20 000 Hz (20 kHz), the audible range; children usually hear higher tones than their grandparents can. Below 20 Hz lies infrasonic sound (infrasound), and above 20 kHz lies ultrasonic sound (ultrasound) Fig. 10.13. Other animals tune in where we cannot. A dog hears the squeak of a "silent" whistle, bats, cats and dolphins hear ultrasound, and elephants rumble to one another in infrasound across kilometres of forest.

Loudness is our sense of how strong a sound is, and it follows amplitude. A shout makes big swings in density and sounds loud, a whisper makes small ones and sounds soft. Walk away from a loudspeaker and it seems quieter, because less intensity reaches you. Intensity and loudness are related but not the same thing. Two people standing at one spot receive the same intensity, yet the one with weaker hearing finds the sound less loud.

A sound with just one frequency, such as a tuning fork or a phone's test beep, is a tone. Real music is richer. A note sung by a singer or played on a harmonium mixes a lowest frequency, the fundamental, with higher ones called overtones. Its graph therefore has a bumpier shape that still repeats Fig. 10.14. The sitar takes this further: beneath its main strings run extra strings (taraf) that are never plucked but hum along in sympathy and thicken the mix.

Hear one note played equally loudly on a violin, a shehnai and a harmonium, and you can still name each instrument with your eyes shut. That difference in character is called timbre (say "tam-ber"). It depends on which overtones are present and how strong each one is, and that in turn depends on the instrument's shape, material and build. Two notes whose fundamental frequencies are in the ratio 2 : 1, such as 220 Hz and 440 Hz, are an octave apart, just like Sa and the upper Sa in Activity 10.7.

10.7 Reflection of Sound

Sound that meets a wall, a hillside or the surface of a lake does not simply vanish: much of it bounces back. This is the reflection of sound, and it follows the rules you learnt for light in Grade 8. Measured from the normal (the line at right angles to the surface), the reflected sound leaves at the same angle as the incoming sound arrived. Also, the incoming direction, the reflected direction and the normal lie in one plane.

You can try this with two long cardboard tubes and a hard board: send the tick of a clock down one tube and listen at the end of the other. The tick is loudest when the two tubes make equal angles with the normal.

10.7.1 Echo

Call out across a deep valley in the hills, or towards a big dam wall, and your own voice answers you a moment later. That answering sound is an echo.

The catch is timing. Your brain blends two sounds into one if the second follows within about a tenth of a second (0.1 s): clap twice very quickly and you hear one blurred clap. So an echo is heard only if the reflection comes back at least 0.1 s after the original. In a classroom the walls are close, the reflections return far sooner than that, and they simply merge with your voice. This rule tells us how far away a reflecting surface must be.

The surface matters too. Bare rock, concrete and glass send most of the sound straight back, so their echoes are crisp. A hillside covered in trees breaks the sound up and scatters it in many directions. A room full of cushions, carpets and drapes swallows much of it, so any echo is faint or smeared.

10.7.2 Reverberation

Clap once in an empty school hall and listen: the sound does not stop dead but hangs in the air for a moment. It is bouncing from wall to ceiling to floor and back, again and again, losing a little energy at each bounce. These reflections reach you only a few hundredths of a second apart (less than about 0.05 s), so they blur into a fading tail instead of separate echoes. This lingering is called reverberation.

Designers of concert halls and auditoriums aim for just the right amount. A little reverberation makes music sound full and warm; too much turns a speech into mush. So they shape curved reflectors behind the stage to throw sound towards the back rows, and they tame stray reflections with padded seats, carpets, heavy curtains and sound-absorbing panels.

10.8 Ultrasonic and Infrasonic Waves, and their Applications

Sounds we cannot hear are still sound waves, and they have become powerful tools in science, medicine and industry.

10.8.1 Echolocation

Back to the bat on a moonless night. Most bats hunt by sound: as one flies, it calls out in short bursts of ultrasound, about ten a second, far too high for us to hear. Every moth, twig and wall throws back a faint echo. The delay tells the bat how far away the object is, and the difference between its two ears tells it which side. As it closes in on a moth, it calls faster and faster, up to about two hundred calls a second. Finding things by their echoes like this is called echolocation. Dolphins and toothed whales hunt the same way under water, and oilbirds and some swiftlets use echoing clicks to fly through pitch-dark caves.

Ships use the same idea under water in sonar (sound navigation and ranging). A transmitter under the hull sends a pulse of ultrasound into the water, and a receiver picks up the echo Fig. 10.17. Sound in seawater travels at a known speed, so the time until the echo gives the distance, using (10.3). Repeated pulses reveal the direction and speed of a submarine, a shoal of fish or a wreck.