Waves and sound for NDA

Sound is a compact chapter in the NDA syllabus, which names "sound waves and their properties" and "simple musical instruments". It is high-yield because the questions repeat their ideas: sound needs a medium, travels fastest in solids, has pitch set by frequency and loudness set by amplitude, and bounces back as an echo. Add the Doppler effect, resonance and how a sitar or flute changes pitch, and you have most of what gets asked.

The numericals are all one-step: v = fλ, an echo distance, a SONAR depth, a lightning-and-thunder gap. They are easy marks, provided you remember to halve the time for anything that goes out and comes back.

Typical question types are:

• transverse versus longitudinal waves;
• v = fλ and T = 1/f;
• the speed of sound in solids, liquids and gases, and the effect of temperature and humidity;
• pitch, loudness and quality, and what each depends on;
• audible range, infrasound and ultrasound, and their uses;
• echo, reverberation and SONAR calculations;
• the Doppler effect and resonance;
• how string, wind and percussion instruments change pitch.

Waves: the basics

A wave carries energy from one place to another without carrying matter along. The particles of the medium only oscillate about their mean positions.

Mechanical waves (sound, water waves) need a medium. Electromagnetic waves (light, radio, X-rays) do not; they cross empty space.

Key terms:

• Amplitude: the maximum displacement from the mean position.
• Wavelength λ: the distance between two consecutive crests (or compressions).
• Frequency f: the number of oscillations per second, in hertz (Hz).
• Time period T: the time for one oscillation; T = 1/f.
• Wave speed: v = fλ.

For a given medium, the speed of sound is fixed, so a higher frequency means a shorter wavelength.

The speed of sound

Sound is a mechanical wave, so it cannot travel through a vacuum. Astronauts on a spacewalk talk by radio.

Sound is fastest in solids and slowest in gases. What changes its speed in air:

• Temperature: speed increases as air gets warmer, by roughly 0.6 m/s for each °C.
• Humidity: moist air is less dense than dry air, so sound travels a little faster on a humid day.
• Pressure: at constant temperature, changing the pressure has no effect.
• Frequency and loudness: no effect. All notes of a song reach you together.

Everyday results: you can hear a distant train by putting an ear to the rail before you hear it through the air. You see lightning before you hear the thunder because light is almost a million times faster. The delay in seconds × 340 gives the distance of the lightning in metres; roughly 3 seconds per kilometre.

Pitch, loudness and quality

Pitch and loudness are independent. A lion's roar is loud but low-pitched; a mosquito's buzz is faint but high-pitched. Prolonged exposure to loud noise damages hearing.

Audible range, infrasound and ultrasound

The human ear hears roughly 20 Hz to 20,000 Hz (20 kHz). The upper limit falls with age.

• Infrasound (below 20 Hz) is produced by earthquakes, volcanic eruptions and large animals such as elephants and whales. Some animals seem to sense it before earthquakes.
• Ultrasound (above 20 kHz) is used by bats to navigate and hunt, and by dolphins. Dogs hear frequencies above our range, which is how a "silent" dog whistle works.

Uses of ultrasound: ultrasonography (imaging the foetus and internal organs, with no ionising radiation), SONAR, cleaning small intricate parts, detecting cracks and flaws in metal blocks, and breaking kidney stones into fine grains.

Echo, reverberation and SONAR

An echo is sound reflected from a large surface. The sensation of a sound lasts about 0.1 s in the ear, so to hear a separate echo the reflected sound must arrive at least 0.1 s later. At about 344 m/s, the sound must travel 34.4 m there and back, so the reflecting surface must be at least about 17 m away.

For any echo calculation: distance = speed × time ÷ 2, because the sound goes to the surface and back.

Reverberation is the persistence of sound in a hall due to repeated reflections. Too much makes speech blurred, so auditoriums use curtains, carpets, soft seats and sound-absorbing panels. Multiple reflection is useful too: it carries sound along the tube of a stethoscope and focuses it from a megaphone.

SONAR (Sound Navigation and Ranging) sends ultrasound pulses under water and times the echo to find the depth of the sea or locate submarines, shoals of fish and wrecks. A fathometer measures sea depth this way.

Doppler effect

When a source of sound and a listener move relative to each other, the frequency heard changes. Approaching, the pitch rises; moving apart, it falls. A train's whistle or an ambulance siren drops in pitch as it passes you.

The same principle is used in police radar speed guns, Doppler radar for weather, Doppler ultrasound to measure blood flow, and, with light, to show that distant galaxies are moving away from us (the red shift).

Resonance and musical instruments

Every object has a natural frequency. If it is pushed by a periodic force at exactly that frequency, it vibrates with a very large amplitude. This is resonance.

• Soldiers break step while crossing a bridge so that their marching does not match the bridge's natural frequency.
• A singer's sustained note can, in principle, shatter a wine glass.
• Tuning a radio matches the circuit's natural frequency to the station's frequency (electrical resonance).

A bottle being filled with water gives a steadily rising note because the air column above the water keeps getting shorter.

Worked NDA-style MCQs

Q1. A sound wave has a frequency of 500 Hz and a wavelength of 0.68 m. Its speed is:
(a) 340 m/s (b) 735 m/s (c) 34 m/s (d) 680 m/s

v = fλ = 500 × 0.68 = 340 m/s. Answer: (a).

Q2. A person claps near a cliff and hears the echo after 2 s. If sound travels at 340 m/s, the cliff is:
(a) 680 m away (b) 170 m away (c) 1,360 m away (d) 340 m away

Distance = 340 × 2 ÷ 2 = 340 m. Answer: (d).

Q3. A ship's SONAR pulse returns from the sea bed after 4 s. If sound travels at 1,500 m/s in sea water, the depth is:
(a) 6,000 m (b) 3,000 m (c) 1,500 m (d) 375 m

Depth = 1,500 × 4 ÷ 2 = 3,000 m. Answer: (b).

Q4. Thunder is heard 5 s after the flash of lightning. Taking the speed of sound as 340 m/s, the lightning struck about:
(a) 68 m away (b) 340 m away (c) 1.7 km away (d) 17 km away

The light arrives almost instantly, so distance = 340 × 5 = 1,700 m. No halving: the sound travels one way. Answer: (c).

Q5. A sitar player tightens a string. The pitch of the note:
(a) falls (b) stays the same (c) becomes zero (d) rises

Higher tension raises the natural frequency, and pitch depends on frequency. Answer: (d).

Q6. Consider the statements: 1. Sound travels faster in humid air than in dry air. 2. At constant temperature, the speed of sound in air changes with pressure. 3. Sound cannot travel through a vacuum. Which are correct?
(a) 1 and 2 (b) 2 and 3 (c) 1 and 3 (d) 1, 2 and 3

Statement 2 is false: pressure alone does not change the speed. Answer: (c).

Common mistakes

• Forgetting to halve the time in echo and SONAR questions, or halving it for lightning.
• Linking loudness to frequency. Loudness depends on amplitude; pitch depends on frequency.
• Calling sound transverse. In air it is longitudinal.
• Saying sound is faster in dry air. Humid air carries it slightly faster.
• Mixing up the ranges. Infra is below 20 Hz; ultra is above 20 kHz.

Practice set

1. Sound waves in air are: (a) longitudinal (b) transverse (c) electromagnetic (d) both transverse and longitudinal
2. A wave has a time period of 0.02 s. Its frequency is: (a) 20 Hz (b) 200 Hz (c) 0.02 Hz (d) 50 Hz
3. The loudness of a sound depends on its: (a) frequency (b) wavelength (c) amplitude (d) speed
4. Bats find their way in the dark using: (a) infrasound (b) infrared (c) audible sound (d) ultrasound
5. Sound travels at 340 m/s. A note of frequency 170 Hz has a wavelength of: (a) 0.5 m (b) 2 m (c) 20 m (d) 57,800 m
6. As a bottle is filled with water from a tap, the pitch of the sound: (a) falls (b) rises (c) stays the same (d) first rises then falls
7. We can tell a violin from a flute playing the same note because of their different: (a) quality (b) loudness (c) pitch (d) speed
8. The frequency of an ambulance siren appears to rise as it approaches because of: (a) resonance (b) the Doppler effect (c) reverberation (d) refraction

Answers:

1. (a). Compressions and rarefactions along the direction of travel.
2. (d). f = 1/T = 1/0.02.
3. (c). Pitch depends on frequency.
4. (d). They time the echoes of their own ultrasonic calls.
5. (b). λ = v/f = 340/170.
6. (b). The vibrating air column gets shorter.
7. (a). Quality depends on the waveform.
8. (b). It falls again as the ambulance moves away.

What to do next

• Write the three characteristics (pitch, loudness, quality) with what each depends on and two examples.
• Solve ten numericals: v = fλ, echo, SONAR and lightning, noting which ones need halving.
• Make a small table of the uses of ultrasound and of resonance.
• Revise heat for NDA, then continue to light and optics.