How is sound produced and how does it travel?
Every sound starts with a vibration: a guitar string, your vocal cords, a drum skin, a speaker cone. Touch your throat while humming and you can feel it shake.
The vibrating object pushes the air particles next to it. Those push the next ones, and so on. The particles do not travel to your ear; each one only moves back and forth about its place. What travels is the disturbance (the energy). This moving disturbance is a wave.
Compressions and rarefactions
When the cone moves forward, particles get crowded: a compression (high pressure, high density). When it moves back, particles spread out: a rarefaction (low pressure, low density).
Longitudinal wave
In sound, particles move along the direction the wave travels. Such a wave is called a longitudinal wave. (In a transverse wave, like a wave on a rope, particles move up-down, at right angles to the wave.)
Sound needs a medium
Sound needs particles to push. It travels through solids, liquids and gases, but not through vacuum. If air is pumped out of a jar with a ringing bell inside, the sound fades although the bell still shakes. That is why astronauts talk by radio in space.
Frequency, amplitude, time period and speed
- Wavelength (λ): the distance between two nearby compressions (or two rarefactions). Unit: metre.
- Frequency (f): number of full waves (oscillations) passing a point in one second. Unit: hertz (Hz). 1 Hz = 1 wave per second.
- Time period (T): time for one full wave. T = 1 ÷ f.
- Amplitude (A): the largest change from the normal (how far particles swing, or how much the pressure rises).
Pitch and loudness
Pitch is how shrill or deep a sound feels. It depends on frequency. A whistle or a small bird has high pitch; a lion's roar or a drum has low pitch.
Loudness depends on amplitude. Hit a drum harder: bigger vibrations, bigger amplitude, louder sound. Loudness is measured in decibels (dB).
Quality (timbre) lets us tell a flute from a violin even when both play the same note at the same loudness. It depends on the shape of the wave.
Speed of sound
In one time period the wave moves one wavelength, so v = λ ÷ T = f × λ.
Speed depends on the medium and temperature, not on the frequency. Roughly: air 340 m/s (at about 20–25 °C), water 1500 m/s, steel 5000 m/s. Sound is fastest in solids. Warmer air carries sound a little faster.
Graphs of sound waves
We cannot see air particles, so we draw a graph. Put distance (or time) on the x-axis and density or pressure on the y-axis.
- A crest (peak) of the graph = a compression.
- A trough (valley) = a rarefaction.
- Distance from one crest to the next on a distance graph = wavelength.
- Time from one crest to the next on a time graph = time period.
- Height of the crest from the middle line = amplitude.
Compare two graphs: crests closer together means higher frequency (higher pitch); taller crests means bigger amplitude (louder). Step 2 of the 3D draws this red curve over the moving particles.
Reflection of sound: echo and reverberation
Sound bounces off hard surfaces like light off a mirror: the angle it hits at equals the angle it leaves at.
Echo
An echo is a reflected sound we hear separately. Our brain keeps a sound for about 0.1 s, so the echo must come back at least 0.1 s later. In air at 344 m/s, the sound must travel 344 × 0.1 = 34.4 m in total, so the wall must be at least about 17.2 m away.
Distance to a wall: d = v × t ÷ 2 (divide by 2 because the sound goes and comes back).
Reverberation
In a big hall, sound bounces many times and keeps ringing. This is reverberation. Too much of it makes speech unclear. Halls use curtains, soft seats, carpets and rough boards that soak up sound.
Uses of many reflections
Megaphones and horns send sound forward. Stethoscopes carry a heartbeat to the doctor's ears by many reflections inside a tube. A curved board behind a stage sends sound out to the audience.
Acoustics in historical buildings
Acoustics is the science of how sound behaves in a space. Old builders used it well.
- Gol Gumbaz, Bijapur (Vijayapura): its huge dome makes a whispering gallery. A whisper near the wall runs round the curved dome by many reflections and is heard clearly on the other side. A clap echoes several times.
- Golconda Fort, Hyderabad: a clap under the entrance dome can be heard at the top of the fort, used as a warning signal.
- Open-air theatres of ancient times were shaped like a bowl with rising steps, so an actor's voice reached the last rows without a speaker.
- Temples and domes: curved ceilings gather sound; bells and chants ring for a long time because of reverberation.
Today's concert halls copy these ideas and add sound absorbers where needed.
Range of hearing: infrasound and ultrasound
Humans hear from about 20 Hz to 20,000 Hz (20 kHz). Children hear higher sounds than older people.
Infrasound (below 20 Hz)
Too low for us. Elephants and whales use it to talk over long distances. Earthquakes give out infrasound before the main shock, and some animals seem to sense it. A swinging pendulum or very slow vibration makes infrasound.
Ultrasound (above 20 kHz)
Too high for us. Dogs, bats, dolphins and porpoises can hear it. Uses:
- Medical scans (ultrasonography): see babies, the liver, kidneys and heart (echocardiography) without harm.
- Breaking kidney stones into fine grains.
- Cleaning hard-to-reach parts like spiral tubes and electronic parts in a liquid bath.
- Finding cracks inside metal blocks: ultrasound passes through, but a crack reflects it.
- SONAR (Sound Navigation And Ranging): ships send ultrasound down and time the echo to find sea depth, submarines or fish. Depth = v × t ÷ 2.
- Bats fly and hunt in the dark by listening to ultrasound echoes.
Try it at home
Slinky wave: Stretch a slinky (or a long spring) on the floor with a friend. Push one end forward and back quickly. Watch the crowded part run along: that is a compression, just like step 1.
String phone: Join two paper cups with a 5 m thread held tight. Speak into one. Sound travels better through the tight thread (a solid) than through air.
Pitch test: Hold a steel ruler on a table edge and twang it. Make the free part shorter: predict, then check that the pitch goes up (higher frequency). Twang harder: louder, same pitch.
Key formulas and definitions
- v = f × λ
- T = 1 ÷ f
- f = 1 ÷ T (Hz)
- Echo / SONAR: distance = v × t ÷ 2
- Minimum distance for echo ≈ 17.2 m (v = 344 m/s)
- Audible range: 20 Hz – 20 kHz
Worked examples
1. A sound wave has frequency 500 Hz and wavelength 0.68 m. Find its speed.
v = f × λ = 500 × 0.68 = 340 m/s.
2. A sound has a time period of 0.002 s. Find its frequency.
f = 1 ÷ T = 1 ÷ 0.002 = 500 Hz.
3. Sound of frequency 170 Hz travels in air at 340 m/s. Find its wavelength.
λ = v ÷ f = 340 ÷ 170 = 2 m.
4. A boy claps in front of a cliff and hears the echo after 2 s. Speed of sound = 340 m/s. How far is the cliff?
Sound goes and returns: total path = 340 × 2 = 680 m. Distance = 680 ÷ 2 = 340 m.
5. A ship's SONAR sends ultrasound and gets the echo from the sea bed after 3 s. Speed of sound in sea water = 1500 m/s. Find the depth.
Depth = v × t ÷ 2 = 1500 × 3 ÷ 2 = 2250 m.
6. Lightning is seen and thunder is heard 4 s later. How far away is the lightning? (v = 340 m/s)
Light arrives almost at once. Distance = 340 × 4 = 1360 m (no ÷ 2, sound travels one way only).
7. A wave has 20 compressions passing a point in 0.1 s. Find its frequency. Can we hear it?
f = 20 ÷ 0.1 = 200 Hz. It lies between 20 Hz and 20,000 Hz, so it is audible.
8. Why is the least distance for a clear echo about 17 m?
The echo must return after at least 0.1 s. Total path = 344 × 0.1 = 34.4 m, half of which is the distance to the wall: 17.2 m.
Common mistakes
- Thinking air particles travel from the source to the ear. They only move back and forth; the energy travels.
- Mixing up pitch and loudness. Pitch = frequency, loudness = amplitude.
- Forgetting to divide by 2 in echo and SONAR problems (sound goes and returns).
- Thinking a higher frequency sound travels faster. In one medium all frequencies travel at the same speed; λ gets shorter instead.