Sound — review

Answerb) a vibrating object

Every sound begins with something moving back and forth. Steady motion is not enough — a car rolling smoothly makes noise from its vibrating parts, not from the motion itself. Stop the vibration and the sound stops instantly, which is what you feel when you grip a struck tuning fork.

Answerd) a vacuum

Sound is particles shoving other particles, so it needs particles. A vacuum has none, and there is nothing to hand the compression on to. This is what the bell jar demonstrates: as the air is pumped out the ringing fades to silence, while the light from the same jar reaches you undimmed.

Answerb) longitudinal wave, with particles moving along the direction of travel

The particles oscillate back and forth along the same line the wave travels, which is what makes it longitudinal. A wave on a rope is transverse — the rope moves up and down while the wave goes sideways. And nothing flows from source to ear: each particle stays about where it was, as the red particle in Fig. 1 shows.

Answerb) frequency

More vibrations per second means more waves per second reaching you, and a higher pitch. Amplitude decides loudness instead, and the two are independent — which is why the trace in Fig. 3 keeps exactly the same height as its pitch climbs.

Answerb) loudness

Amplitude is how far the particles are pushed from their rest positions, and that is what loudness measures. Since the frequency is the same, the pitch is the same; and since the medium is the same, so are the speed and the wavelength.

Answerc) hertz

One hertz is one complete wave per second. The second is the unit of the time period, which is frequency upside down; the decibel measures loudness, not frequency.

Answerc) steel

Sound travels fastest where particles are closest together and most tightly bound, because each one passes the push on sooner. So solids beat liquids beat gases: roughly 5960 m/s in steel, 1500 m/s in water, 344 m/s in air.

Answerb) 0.005 s

Frequency counts waves per second; the period is seconds per wave. Each is the other upside down, so T = 1/f = 1/200 = 0.005 s. Answering 200 s is reading the relationship the wrong way round.

Answerb) 17.2 m

The sensation of a sound lasts about 0.1 s in your brain, so the reflection must take at least that long to return. In 0.1 s sound covers 344 × 0.1 = 34.4 m — but that is the round trip, so the wall is half of it: 17.2 m. Answering 34.4 m is forgetting that the sound goes there and back.

Answerb) 20 Hz to 20 000 Hz

Twenty hertz to twenty kilohertz — a factor of a thousand from bottom to top. The upper limit falls with age, so most adults hear rather less than 20 kHz.

Answerb) ultrasound

Above 20 000 Hz is ultrasound; below 20 Hz is infrasound. Note that neither word says anything about loudness — an ultrasonic pulse can be extremely intense and you still will not hear it, because it is outside the band your ear responds to.

Answerb) (v × t) / 2

The pulse travels down to the sea bed and back up again, so v × t is twice the depth. Halving it gives the depth. Forgetting to divide by two is the commonest mistake in every echo and SONAR question.

Answerc) cochlea

Everything before the cochlea is mechanical — air pushing the eardrum, the eardrum pushing the three bones. The cochlea, in the inner ear, is where that vibration becomes an electrical signal. The auditory nerve then carries that signal, but it does not create it.

Answerb) hammer, anvil, stirrup

Hammer, then anvil, then stirrup — the hammer is attached to the eardrum, so it goes first, and the stirrup passes the vibration on to the inner ear. Their job is to amplify the vibration several times over; the cochlea is not a bone and belongs to the inner ear.

Sound travels because particles of the medium are pushed and pass the push on to their neighbours; with no particles there is nothing to carry it. The experiment is the bell jar: an electric bell is suspended inside a sealed glass jar connected to a vacuum pump and switched on, so it can clearly be heard. As the air is pumped out the sound grows fainter and fainter, and when the jar is nearly evacuated no sound is heard at all — although the hammer can still be seen striking the gong, so the bell is certainly still ringing. Let air back in and the sound returns. Since only the air was removed, the air must be what was carrying the sound.

A longitudinal wave is one in which the particles of the medium oscillate back and forth along the same direction in which the wave travels. Sound in air is longitudinal because a vibrating object alternately pushes the air in front of it together, making a compression, and moves away leaving it spread out, making a rarefaction — and these regions travel forwards along the same line as the particle motion. In a transverse wave, such as a wave on a stretched rope, the particles move at right angles to the direction of travel: the rope moves up and down while the wave moves sideways.

Wavelength is the distance between two consecutive compressions (or two consecutive rarefactions) — one complete repeat of the wave — and is measured in metres. Frequency is the number of complete waves passing a point in one second, measured in hertz, and equals the number of vibrations per second of the source. Time period is the time taken for one complete wave to pass a point, measured in seconds. Amplitude is the maximum displacement of a particle of the medium from its rest position. Frequency and time period are reciprocals: T = 1/f.

Loudness is how strong a sound seems, and it is determined by the amplitude of the wave: a larger amplitude means the particles are displaced further, the sound carries more energy, and it is heard as louder. Pitch is how high or low a sound seems, and it is determined by the frequency: a higher frequency is heard as a higher pitch. The two are independent — a high note may be quiet and a low note deafening — because amplitude and frequency are separate properties of the same wave.

The sensation of a sound persists in the brain for about 0.1 s. For a reflection to be heard as a separate sound it must arrive after that interval, which at 344 m/s requires the reflecting surface to be at least 17.2 m away, since the sound must travel there and back. In a small room the walls are only a few metres away, so the reflection returns well within 0.1 s and merges with the original — you hear a single sound rather than two.

Reverberation is the persistence of sound in a large hall caused by repeated reflection from the walls, ceiling and floor, so that reflections continue to arrive after the original sound has stopped. Excessive reverberation makes speech unclear because each word is still echoing while the next is being spoken. It is reduced by covering surfaces with sound-absorbing materials — curtains, carpets, and seats with cushioned or fabric coverings — and by using rough, panelled or perforated surfaces on the walls and ceiling, which absorb sound rather than reflecting it cleanly back.

Three uses: cleaning objects with hard-to-reach parts such as spiral tubes; detecting cracks and flaws inside metal blocks; and forming images of internal organs, as in ultrasonography and echocardiography. Taking crack detection in detail: ultrasonic waves are passed through a metal block while detectors monitor the transmitted beam. Ultrasound travels through sound metal, but a crack or an air gap inside reflects it, so less of the beam reaches the detector beyond that point. A defect invisible from the outside therefore shows up as a gap in the transmitted signal — which matters because such flaws would weaken a structure and could lead to failure.

The ear works in three sections. The OUTER EAR begins with the pinna, whose funnel shape collects sound from a wide area and directs it into the auditory canal, a tube that carries the sound inward to the eardrum. The eardrum is a thin stretched membrane: when a compression arrives the pressure outside it rises and pushes it inward, and when a rarefaction arrives it moves back outward, so it vibrates at the frequency of the sound. In the MIDDLE EAR, three small bones — the hammer, the anvil and the stirrup, in that order — amplify these vibrations several times and pass them to the inner ear. In the INNER EAR, the cochlea converts the pressure variations into electrical signals, which the auditory nerve carries to the brain. The brain interprets those signals as sound. Note the key change: everything up to the cochlea is mechanical, and from the cochlea onward it is electrical.

1. Formulav = f × λ
2. Substitutev = 220 × 1.5

Answerv = 330 m/s

The equation is just common sense written down: the length of one wave times the number of waves per second is how far the wave gets in a second. Check the unit as a sanity test — hertz is per second, so Hz × m gives m/s.

1. FormulaT = 1 / f
2. SubstituteT = 1 / 500

AnswerT = 0.002 s (2 ms)

Frequency is waves per second and period is seconds per wave, so each is the other upside down. Answering 500 s means the relationship was read the wrong way round — always sanity-check that a period comes out small when the frequency is large.

1. Total pathtotal distance = v × t = 344 × 3
2. total distance = 1032 m
3. Halve itd = 1032 ÷ 2

Answerd = 516 m

The sound travelled to the cliff and back, so the 1032 m is twice the distance to it. Quoting 1032 m is the mistake this question is built to catch — whenever you are given a time for an echo, ask whether the sound made a round trip.

1. Total pathtotal distance = v × t = 1531 × 5
2. total distance = 7655 m
3. Halve itd = 7655 ÷ 2

Answerdepth = 3827.5 m

Exactly the same structure as the cliff: the pulse goes down and comes back, so the depth is half the distance travelled. Note the speed used is the one for sea water, not for air — using 344 m/s here would give an answer roughly four times too small.

1. Rearrangev = f λ, so λ = v / f
2. At 20 Hzλ = 344 ÷ 20
3. At 20 kHzλ = 344 ÷ 20 000

Answerλ = 17.2 m and λ = 0.0172 m (1.72 cm)

A thousandfold change in frequency gives a thousandfold change in wavelength, because the speed of sound in air is fixed by the air and not by the note. That 17.2 m is a coincidence of arithmetic and has nothing to do with the 17.2 m minimum distance for an echo — one comes from dividing by 20 Hz, the other from 0.1 s of hearing persistence.