Sound Waves and Hearing

Sound is a longitudinal wave — the particles of the medium vibrate parallel to the direction of energy transfer.

When a speaker vibrates:

1. It pushes air particles together → compression (high pressure)
2. It pulls back, leaving a gap → rarefaction (low pressure)
3. These compressions and rarefactions travel outwards through the air

The particles themselves don't travel — they oscillate back and forth, passing energy from one to the next.

Sound travels at different speeds in different media:

Sound is fastest in solids (particles close together, transfer energy quickly) and slowest in gases (particles far apart).

Measuring the Speed of Sound

Method 1 — Echo method:

1. Stand a measured distance $d$ from a large wall
2. Clap and time how long ($t$) it takes to hear the echo
3. $v = 2d/t$ (sound travels there and back)

Method 2 — Two microphones:

1. Place two microphones a known distance apart
2. Make a sharp sound near one end
3. An electronic timer measures the time difference
4. $v = d/t$

Human Hearing Range

Humans can typically hear sounds between 20 Hz and 20,000 Hz (20 kHz).

• Below 20 Hz: infrasound (elephants, earthquakes)
• Above 20,000 Hz: ultrasound (bats, dog whistles, medical imaging)

Hearing range decreases with age — older people may not hear above ~16,000 Hz.

Ultrasound is sound with a frequency above 20,000 Hz — beyond human hearing.

Applications

Medical imaging (pregnancy scans):

• Ultrasound pulses are sent into the body
• They reflect off boundaries between different tissues
• The time delay and intensity of reflections build up an image
• Safe — no ionising radiation (unlike X-rays)

Industrial quality control:

• Ultrasound detects cracks or flaws inside metal structures
• Pulses reflect off internal defects

Distance measurement (sonar):

• Used by ships to measure ocean depth
• Pulse sent down, echo detected $d = \frac{v \times t}{2}$

Cleaning:

• Ultrasonic cleaners vibrate dirt off delicate objects (jewellery, surgical instruments)

Echo: A reflection of sound off a hard surface that is heard as a separate, distinct sound. Requires the reflecting surface to be at least ~17 m away (for a time delay > 0.1 s).

Reverberation: When sound reflects off many surfaces and the reflections overlap, creating a prolonged sound. Common in large halls.

• Too much reverberation → muddy sound, poor clarity
• Too little reverberation → dry, unnatural sound
• Solutions: soft furnishings, acoustic panels absorb sound and reduce reverberation

1. Sound waves enter the ear canal
2. They cause the eardrum to vibrate
3. Vibrations pass through three small bones (hammer, anvil, stirrup) — these amplify the signal
4. Vibrations reach the cochlea (fluid-filled spiral)
5. Hair cells in the cochlea convert vibrations to electrical signals
6. Signals travel along the auditory nerve to the brain

Hearing Damage

• Prolonged exposure to loud sounds (>85 dB) can damage hair cells permanently
• Hearing loss is irreversible
• Prevention: ear protection, volume limits on devices

• Sound is a longitudinal wave — compressions and rarefactions
• Needs a medium — cannot travel through a vacuum
• Speed: fastest in solids, slowest in gases (~340 m/s in air)
• Pitch ∝ frequency; loudness ∝ amplitude
• Human hearing: 20 Hz to 20 kHz; above 20 kHz = ultrasound
• Ultrasound applications: medical imaging, sonar, cleaning
• Echoes: $d = vt/2$