Sound

Sound covers about 343 metres each second in air at 20 °C, so thunder 3 seconds after a flash means the lightning was about 1 km away.

Pressure waves in the air

When a drum skin moves outward it squeezes the air next to it, and when it moves back it leaves a region of slightly lower pressure. Those squeezes and stretches pass from molecule to molecule as a longitudinal wave. The air near your ear does not travel from the drum to you; it shuffles back and forth by a tiny amount while the pressure pattern moves on. OpenStax notes that at the quietest sound a person can hear, the air molecules move back and forth by less than one molecular diameter.

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Sound in a 2 m tube. The orange curve is the air pressure; the dots are air molecules (drawn far apart and slowed right down). Change the frequency, the air temperature or the medium, and press Play tone to hear the note.

How fast is sound?

You can see that sound takes time at a fireworks display: the flash comes first and the bang arrives later. OpenStax gives the speed of sound in air as 331 m/s at 0 °C and 343 m/s at 20 °C, and a formula for air at sea level: v = 331 m/s × √(T / 273 K), with T in kelvin. Warmer air means faster molecules, which pass the push along more quickly, but the effect is gentle. Going from 0 °C to 20 °C raises the speed by less than 4%. A useful rule follows from 343 m/s: sound needs about 3 seconds to cover a kilometre, so counting the seconds between lightning and thunder gives the distance.

Sound goes faster in liquids and solids than in air, because they are much harder to compress. The speed depends on how stiff a material is and how dense it is: stiffer means faster, and for similar stiffness the lighter material wins. OpenStax lists values for many materials. Rubber is an exception at the slow end because it is so soft.

Medium	Speed of sound (m/s)
Air, 0 °C	331
Air, 20 °C	343
Helium, 0 °C	965
Fresh water, 20 °C	1480
Sea water, 20 °C	1540
Steel	5960
Vulcanized rubber	54

Pitch, the range of hearing and echoes

The frequency of a sound is heard as its pitch. People with good hearing can usually hear from about 20 Hz to 20 000 Hz. Sounds above that range are called ultrasound and those below are infrasound. Within the audible range the speed hardly depends on frequency. OpenStax makes the case with a marching band: if high notes travelled faster than low ones, the music would arrive out of step for listeners far away, and it does not.

Sound reflects from hard surfaces, and the returning sound is an echo. If you clap in front of a cliff and hear the echo 2 seconds later, the sound has gone there and back, so the cliff is 343 × 2 ÷ 2 ≈ 343 m away. Bats use echoes to find insects, and medical ultrasound uses the echoes of very high frequencies from inside the body. Because the wavelengths of audible sound run from centimetres to many metres, sound also bends around doorways and corners, which is why you can hear someone in the next room without seeing them.

Loudness and decibels

Loudness follows the intensity of the wave, the power it carries through each square metre. The ear covers a huge range: the faintest sound at 1000 Hz has an intensity of about 10⁻¹² W/m², and a sound that damages hearing in seconds is about 10¹² times stronger. To keep the numbers manageable we use the decibel scale, β = 10 log₁₀(I / I₀) with I₀ = 10⁻¹² W/m². Every factor of 10 in intensity adds 10 dB, and doubling the intensity adds about 3 dB. OpenStax lists normal conversation near 60 dB and a loud rock concert near 120 dB, the threshold of pain. Its footnote adds that several government and health agencies recommend not exceeding 85 dB for 8 hours a day without hearing protection.

BackgroundThe bel, the unit behind the decibel, is named after Alexander Graham Bell, the inventor of the telephone. A decibel is a tenth of a bel. The scale was chosen because our sense of loudness follows the logarithm of intensity much better than the intensity itself, so equal steps in decibels feel like roughly equal steps in loudness.

Use v = 331 m/s × √(T/273 K). What is the speed of sound at 30 °C (303 K)? One decimal place.
You see lightning and hear thunder 6.0 s later. With sound at 343 m/s, how far away was the strike, in km? Two decimal places.
You clap in front of a cliff and hear the echo 2.0 s later. Sound travels at 343 m/s. How far away is the cliff?
In which of these does sound travel fastest?
- Steel
- Fresh water
- Air at 20 °C
- Helium
Why can astronauts not hear each other shout across empty space?
- Sound needs a medium to travel through
- Sound travels too fast in space
- Space is too cold for sound
- Their voices are too high
A 90 dB sound compared with a 60 dB sound is how many times more intense?
- 1000 times
- 30 times
- 3 times
- 1.5 times
Two identical speakers play the same sound, doubling the intensity. The level rises by about…
- 3 dB
- 10 dB
- 2 dB
- 20 dB
At 20 °C (343 m/s), what is the wavelength of the lowest sound people can hear, 20 Hz? One decimal place.
Which property of a sound do we hear as its pitch?
- Frequency
- Amplitude
- Speed
- Temperature
In a sound wave in air, the air molecules…
- Move back and forth along the direction of travel
- Fly from the source to your ear
- Move up and down across the direction of travel
- Stay perfectly still

Key points

Sound is a longitudinal pressure wave and needs a medium.
In air: 331 m/s at 0 °C, 343 m/s at 20 °C; v = 331 √(T/273 K).
Faster in liquids and solids: water 1480 m/s, steel 5960 m/s.
Hearing: about 20 Hz to 20 000 Hz. +10 dB = 10 × intensity, +3 dB ≈ 2 ×.

Sources for this course (11)

OpenStax College Physics 2e (openstax.org/books/college-physics-2e): 16.9 Waves (disturbance that propagates, gull example λ 10.0 m, T 5.00 s, v = 2.00 m/s, transverse and longitudinal, amplitude independent of speed)
16.10 Superposition and Interference (constructive, destructive, standing waves, f1 = v/2L, beats fB = |f1 − f2|, 256 Hz fork with 2 beats -> 254 or 258 Hz)
17.2 Speed of Sound (Table 17.1: air 331 m/s at 0 °C, helium 965, fresh water 1480, sea water 1540, steel 5960, vulcanized rubber 54; v = 331 m/s × √(T/273 K); 343 m/s at 20 °C; audible range 20 to 20 000 Hz; P-waves 4 to 7 km/s, S-waves 2 to 5 km/s; Oldham and Lehmann)
17.3 Sound Intensity (I0 = 10⁻¹² W/m², Table 17.2, factor 10 = 10 dB, factor 2 = 3 dB, 85 dB for 8 h footnote, bel named for Bell)
17.5 Sound Interference and Resonance (noise-cancelling headphones 30 dB or more, closed tube λ = 4L and f_n = n v/4L with n odd, open tube f_n = n v/2L, 128 Hz tube at 22 °C = 0.672 m, ninth harmonic 1.15 kHz, trumpet vs clarinet overtones)
24.1 (Maxwell; Hertz from 1887)
24.3 The Electromagnetic Spectrum (c = fλ, Table 24.1, three rules of thumb, AM 540 to 1600 kHz, FM 88 to 108 MHz, microwave oven 2.45 GHz, visible 400 to 750 nm, UV 400 to about 10 nm, UV-A 320 to 400, UV-B 290 to 320, UV-C 220 to 290 nm, 99% of surface UV is UV-A, X-rays below 0.01 nm)
27.3 Young's Double Slit (1801, d sin θ = mλ, 0.0100 mm and 633 nm example)
NASA science.nasa.gov/ems (Introduction, Visible Light: 380 to 700 nm; atmospheric windows)
NIST, c = 299 792 458 m/s exact (nist.gov/si-redefinition/meter)
ISO 16:1975 (A = 440 Hz, iso.org/standard/3601.html).

Checked: 2026-10-17