Sound speed and wavelength
Key idea: When sound passes into a different medium, its frequency stays the same but its speed and wavelength change. In the same air, a higher frequency means a shorter wavelength.
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Guided lessons · coming soon
Guided lesson
Guided steps
- Compare sound speeds in air, water and steel.
- Identify one wavelength, then connect speed, frequency and wavelength.
- Follow the rearrangement and units before comparing neighbouring compression spacing.
- Find the wavelength and frequency, then calculate the sound speed.
- Choose the correct rearrangement and calculate the frequency.
- Read why frequency stays the same when sound enters a different medium.
- Identify what stays the same and calculate the wavelength in air and water.
- Count the spaces between compressions, then find the speed and the new wavelength.
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ContinueIn a thunderstorm you see the lightning before you hear the thunder, because light is almost a million times faster than sound. Sound in air travels at roughly 340 m s⁻¹, but it is faster in water and faster still in most solids. Knowing the speed, the wave equation gives the wavelength or frequency of any sound.
How fast sound travels
| Medium | Typical speed of sound |
|---|---|
| air at room temperature | about 340 m s⁻¹ |
| water | about 1500 m s⁻¹ |
| steel | about 5000 m s⁻¹ |
Sound is usually fastest in solids and slowest in gases. In a solid, the particles are close together and strongly linked, so each one passes the push on to its neighbours very quickly. In a gas, the particles are far apart and only pass the disturbance on when they collide.
The speed of sound in air also rises with temperature. These values are typical: in a calculation, always use the speed the question gives.
The speed of sound is how fast the compressions travel. The air particles themselves only vibrate to and fro by tiny distances.
Wavelength and the wave equation
The wavelength of a sound is the distance between the centres of two neighbouring compressions (or rarefactions). A compression and the next rarefaction are only half a wavelength apart. Count the spaces between compressions: four consecutive compressions span three wavelengths.
Sound obeys the wave equation like every other wave:
In the same air at the same temperature, sound speed stays the same. A higher-frequency sound therefore has a shorter wavelength.
Worked example 1
The wavelength of a note
Problem
Show full solution
Rearrange the wave equation
Method
Make the wavelength the subject of v = fλ.Reason
You know the speed and the frequency.Working
Answer
λ = v/fSubstitute
Method
Divide the speed by the frequency.Reason
The sound travels 340 m each second, shared between 680 waves.Working
Answer
λ = (340 m s⁻¹)/(680 Hz) = 0.50 m
Quick check
Check your understanding 1 Speed from the spacing of compressions
A source vibrates 170 times each second. The centres of neighbouring compressions in the sound it makes are 2.0 m apart. Find the speed of the sound.
Show answer
Neighbouring compressions are one wavelength apart, so λ = 2.0 m and f = 170 Hz:
Spot the mistake 2
Rearranging for frequency
Learner response
Diagnose, then calculate
Show solution step by step
Make frequency the subject
Method
Divide the speed by the wavelength.Reason
In v = fλ, the frequency is multiplied by λ, so you undo that by dividing.Working
Answer
f = v/λCalculate
Method
Substitute the values.Reason
Metres per second divided by metres leaves “per second”, which is hertz.Working
Answer
f = (340 m s⁻¹)/(0.85 m) = 400 Hz
Common mistake
Sound passing into a different medium
When sound passes from one medium into another, across a stationary boundary, its speed changes but its frequency does not: the waves arriving each second are the waves that cross into the new medium each second. Since λ = v/f, the wavelength changes in proportion to the speed.
Check your understanding 2 From air into water
A 500 Hz sound passes from air, where its speed is 340 m s⁻¹, into water, where its speed is 1500 m s⁻¹. Which quantity stays the same? Find the wavelength in each medium.
Show answer
The frequency stays at 500 Hz.
In air: λ = (340 m s⁻¹)/(500 Hz) = 0.68 m
In water: λ = (1500 m s⁻¹)/(500 Hz) = 3.0 m
The sound is faster in water, so at the same frequency each wave is longer.
Check your understanding 3 Several compressions in one measurement
A 1.0 kHz sound has four consecutive compressions spanning 1.02 m in air. Find its wavelength and speed. The sound enters water, where its speed is 1500 m/s. Find the wavelength in water.
Show the steps Optional working
Show the steps Optional working
Show answer
Four compressions span three wavelengths, so λₐᵢᵣ = 1.02/3 = 0.34 m. The frequency is 1.0 kHz = 1000 Hz, giving v = 1000 × 0.34 = 340 m s⁻¹.
In water the frequency is still 1000 Hz, so λ_water = 1500/1000 = 1.5 m. The faster speed increases the spacing of compressions; it does not increase the source frequency.
Common mistakes
- Using 340 m s⁻¹ when the question gives a different speed, or for sound in water.
- Measuring a wavelength from a compression to the next rarefaction. That is half a wavelength.
- Saying a higher-pitched sound travels faster. In the same air, all sounds travel at the same speed.
- Saying the frequency changes when sound enters a new medium. The speed and wavelength change; the frequency stays the same.
- Mixing up the speed of the wave with the speed of the vibrating air particles.
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Syllabus and review details
- SEC G3 Physics 2027 · 2027
Content Structure, PDF page 9; Subject Content, PDF pages 10–28