Sound Waves and Hearing

Every sound you have ever heard — a whisper, a thunderclap, a favourite song — reached you as a wave travelling through the air. Sound is a longitudinal wave: a travelling pattern of squashed and stretched air that your ear turns into the sensation of hearing. Because it needs particles to carry it, sound cannot travel through the vacuum of space — which is why, despite the films, an explosion in space would be silent. This lesson, part of Topic P5 (Waves in matter) of OCR Gateway Science A, explains how sound travels, how fast it goes, the range of frequencies humans can hear, how the ear detects it, and how the pitch and loudness we perceive relate to a sound wave's frequency and amplitude.

By the end of this lesson you should be able to describe sound as a longitudinal wave that needs a medium, state the speed of sound in air and the human hearing range, describe qualitatively how the ear detects sound, link frequency to pitch and amplitude to loudness, interpret oscilloscope traces, and carry out wave-equation calculations for sound.

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Sound as a Longitudinal Wave

A sound wave is a longitudinal wave. When an object vibrates — a loudspeaker cone, a guitar string, your vocal cords — it pushes and pulls on the air next to it. Pushing forward squashes the air particles together into a compression (high pressure); pulling back leaves them spread apart in a rarefaction (low pressure). These compressions and rarefactions travel outward through the air as a sound wave, with the air particles oscillating back and forth along the same direction the wave travels.

As with every wave, the air particles themselves do not travel from the source to your ear; they merely oscillate about their fixed positions, passing the energy along from one particle to the next. The voice of a person across a room reaches you as energy carried by the air, not as air blown from their mouth to your ear.

Because sound is carried by vibrating particles, it must travel through a medium — a solid, liquid or gas. It cannot travel through a vacuum, because there are no particles to compress and rarefy. This is the classic demonstration with an electric bell ringing inside a sealed jar: as the air is pumped out, the sound fades to nothing even though you can still see the hammer striking, because there is less and less air to carry the sound.

Sound generally travels fastest in solids, slower in liquids, and slowest in gases, because in solids the particles are closest together and pass the vibration on most quickly.

Exam Tip: Sound is longitudinal and needs a medium. The bell-in-a-jar demonstration is the standard evidence that sound cannot travel through a vacuum: as the air is removed, the sound dies away even though the bell is still vibrating.

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The Speed of Sound in Air

In air, sound travels at roughly $330$330 to $340 \text{ m/s}$340 m/s (about $1200 \text{ km/h}$1200 km/h). This is fast, but far slower than light. That difference explains why, in a thunderstorm, you see the lightning before you hear the thunder: light reaches you almost instantly, but the sound takes several seconds to cover each kilometre. You can even estimate how far away a storm is by counting the seconds between the flash and the rumble.

The speed of sound depends on the medium and its temperature, but for OCR you can take it as about $340 \text{ m/s}$340 m/s in air unless a question gives you a different value.

Worked Example 1 — Wavelength of a sound

A loudspeaker produces a sound of frequency $170 \text{ Hz}$170 Hz. The speed of sound in air is $340 \text{ m/s}$340 m/s. Calculate the wavelength.

Step 1 — rearrange the wave equation for wavelength: $\lambda = \dfrac{v}{f}$λ=fv​.

Step 2 — substitute: $\lambda = \dfrac{340}{170}$λ=170340​.

Step 3 — calculate: $\lambda = 2 \text{ m}$λ=2 m.

Answer: the wavelength is $2 \text{ m}$2 m.

Worked Example 2 — Frequency of a sound

A sound wave in air has a wavelength of $0.17 \text{ m}$0.17 m. Taking the speed of sound as $340 \text{ m/s}$340 m/s, calculate its frequency.

Step 1 — rearrange for frequency: $f = \dfrac{v}{\lambda}$f=λv​.

Step 2 — substitute: $f = \dfrac{340}{0.17}$f=0.17340​.

Step 3 — calculate: $f = 2000 \text{ Hz}$f=2000 Hz.

Answer: the frequency is $2000 \text{ Hz}$2000 Hz ($2 \text{ kHz}$2 kHz).

Exam Tip: For sound calculations use the wave equation $v = f\lambda$v=fλ exactly as for any wave, with the speed of sound (about $340 \text{ m/s}$340 m/s in air) as $v$v. Do not confuse the speed of sound with the speed of light ($3 \times 10^8 \text{ m/s}$3×108 m/s) — they differ by a factor of nearly a million.

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The Human Hearing Range

Humans cannot hear sounds of every frequency. The human hearing range is about $20 \text{ Hz}$20 Hz to $20\,000 \text{ Hz}$20000 Hz ($20 \text{ kHz}$20 kHz):

• sounds below $20 \text{ Hz}$20 Hz are called infrasound — too low for us to hear (some animals, such as elephants, use it);
• sounds above $20\,000 \text{ Hz}$20000 Hz are called ultrasound — too high for us to hear (dogs, bats and dolphins can detect it).

The upper limit of $20 \text{ kHz}$20 kHz is for healthy young ears; it tends to fall with age and with exposure to loud noise, so adults often cannot hear the highest frequencies that children can.

Exam Tip: Learn the hearing range as $20 \text{ Hz}$20 Hz to $20 \text{ kHz}$20 kHz. The reason humans cannot hear ultrasound is simply that its frequency is above $20 \text{ kHz}$20 kHz, the top of our range — a fact you will use again in the ultrasound lesson.

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How the Ear Detects Sound

The human ear converts a sound wave in the air into nerve signals your brain interprets as sound. You only need a qualitative description for OCR:

1. The sound wave (compressions and rarefactions) travels down the ear canal to the eardrum — a thin, taut membrane.
2. The changing pressure of the wave makes the eardrum vibrate back and forth. The vibrations match the sound: a higher-frequency sound makes it vibrate faster, a louder sound makes it vibrate with a bigger movement.
3. These vibrations are passed on and amplified by tiny bones in the middle ear, which transmit them to the inner ear.
4. In the inner ear, the vibrations are converted into electrical nerve signals that travel along the auditory nerve to the brain, where they are interpreted as sound.

The essential idea is that the eardrum vibrates in response to the pressure changes of the sound wave, and these vibrations are eventually turned into signals the brain understands. The ear can only respond to vibrations between about $20 \text{ Hz}$20 Hz and $20 \text{ kHz}$20 kHz, which sets the limits of human hearing.

Exam Tip: Keep the ear description simple and in order: sound wave → eardrum vibrates → vibrations passed on (and amplified) → converted to nerve signals → brain. The key step examiners want is that the eardrum vibrates because of the pressure changes in the wave.

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Pitch and Loudness: Frequency and Amplitude

Two features of a sound wave control how we perceive it: