The speed of sound, explained with examples
Sound travels at about 340 metres per second in air, much more slowly than light. That is why you see lightning before you hear thunder, and why echoes can be used to measure distances. This guide covers everything GCSE Physics asks about the speed of sound.
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How sound travels
Sound is a longitudinal wave. A vibrating source, such as a loudspeaker cone, pushes and pulls on the particles of the medium, creating regions where particles are squashed together (compressions) and regions where they are spread out (rarefactions). The particles vibrate back and forth in the same direction as the wave travels, passing energy along. Sound needs a medium: it cannot travel through a vacuum, because there are no particles to pass on the vibrations. That is why space is silent.
Typical speeds
- Air: about 330 to 340 m/s, depending on temperature (about 343 m/s at 20 °C). Sound is faster in warmer air.
- Water: about 1500 m/s.
- Steel: about 5000 to 6000 m/s.
Sound generally travels fastest in solids and slowest in gases, because the particles in solids are closely linked, so vibrations pass from one to the next very quickly. By comparison, light travels at 300,000,000 m/s, nearly a million times faster than sound in air.
The wave equation
v = f λ
wave speed (m/s) = frequency (Hz) × wavelength (m). The frequency of a sound is set by the source and decides its pitch; the amplitude decides its loudness. When sound passes from air into water, its speed increases and its wavelength increases, but its frequency stays the same.
Worked examples
Example 1: wavelength of a note
A tuning fork produces a note of 440 Hz. Sound travels at 340 m/s. Find the wavelength.
- λ = v/f = 340/440.
- λ ≈ 0.77 m.
Example 2: thunder and lightning
You hear thunder 6 seconds after seeing a lightning flash. How far away was the lightning? (speed of sound = 340 m/s)
- Light arrives almost instantly, so the delay is the time for the sound.
- distance = speed × time = 340 × 6 = 2040 m, about 2 km. A rough rule: every 3 seconds is about 1 km.
Example 3: an echo
A student claps 85 m from a large wall and hears the echo 0.5 s later. Find the speed of sound.
- The sound travels to the wall and back: 2 × 85 = 170 m.
- speed = 170/0.5 = 340 m/s. Forgetting to double the distance is the most common mistake with echoes.
Example 4: sonar
A ship sends an ultrasound pulse to the seabed. The echo returns 0.8 s later. Sound travels at 1500 m/s in sea water. Find the depth.
- Total distance = 1500 × 0.8 = 1200 m, there and back.
- Depth = 1200/2 = 600 m.
Example 5: sound in water
A 500 Hz sound passes from air (340 m/s) into water (1500 m/s). Find its wavelength in each.
- In air: 340/500 = 0.68 m. In water: 1500/500 = 3.0 m.
- The frequency is unchanged at 500 Hz, so the pitch is the same; only the speed and wavelength change.
Measuring the speed of sound
There are several methods, each with its own sources of error.
- Clap and echo: stand a measured distance, such as 50 m, from a large wall. Clap in time with the echoes, so each clap coincides with the echo of the last one. Time 20 claps with a stopwatch; each interval is the time for sound to travel there and back. Timing many intervals reduces the effect of reaction time.
- Two microphones: place two microphones a measured distance apart, connected to a data logger or oscilloscope. Make a sharp sound in line with them; the logger records the time difference precisely. This avoids human reaction time altogether.
- Two people outdoors: one person bangs two blocks together a long distance away, such as 300 m; the other starts a stopwatch on seeing the bang and stops on hearing it. Reaction time is a large error here, so repeat many times and average.
In the GCSE waves required practical, you may also measure the speed of waves on a stretched string or in a ripple tank using v = fλ, measuring the wavelength over several waves to reduce uncertainty.
Ultrasound and hearing
Humans can hear frequencies from about 20 Hz to 20,000 Hz (20 kHz). This range shrinks with age, especially at the high end. Sound above 20 kHz is ultrasound; below 20 Hz it is infrasound. Ultrasound partially reflects at boundaries between different materials, and the time taken for echoes to return reveals how deep each boundary is. This is used for prenatal scans, which are safe because ultrasound is not ionising, and for industrial imaging to find cracks inside metal. Separate Physics students also learn how seismic waves, P-waves and S-waves, travel through the Earth and reveal its structure.
How the ear works
Sound waves reaching the ear make the eardrum vibrate. Tiny bones pass the vibrations to the inner ear, where they are converted into electrical signals for the brain. Separate Physics explains that this conversion only works over a limited frequency range, because of how the eardrum and the structures of the inner ear respond, which is why we cannot hear ultrasound.
Common mistakes
- Forgetting to halve (or double) the distance in echo questions.
- Saying sound travels through a vacuum; it needs a medium.
- Thinking the frequency changes when sound enters a new material; it is the speed and wavelength that change.
- Confusing pitch (frequency) with loudness (amplitude).
Practice questions
Try each one before opening the answer.
Q1. Find the frequency of a sound with wavelength 1.7 m in air (v = 340 m/s).
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Q2. An echo from a cliff returns after 2.0 s. How far away is the cliff? (v = 340 m/s)
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Q3. Is 25 kHz audible to humans?
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Q4. Why can sound not travel in space?
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Frequently asked questions
What value should I use for the speed of sound in GCSE questions?
Use the value given in the question. If none is given, about 330 to 340 m/s in air is typical, but exam questions almost always state it.
Is the speed of sound in Combined Science?
Yes. Sound as a longitudinal wave and v = fλ are in both Combined Science and separate Physics. Ultrasound, echo sounding and seismic waves are mainly separate Physics.
Key takeaways
- Sound is a longitudinal wave that needs a medium.
- About 340 m/s in air, 1500 m/s in water and over 5000 m/s in steel.
- v = fλ; frequency stays the same between materials.
- In echo questions, the sound travels there and back.
- Human hearing: about 20 Hz to 20 kHz; above that is ultrasound.