Speed = wavelength × frequency

The idea

The speed of sound is the distance a crest or trough travels in unit time; as it moves one wavelength in one time period, v = λ / T = λ × ν (speed = wavelength × frequency).

A crest on the move

A wave has a wavelength, and a number of waves pass a fixed point every second.

If 170 waves pass a point each second and each wave is 2 m long, how far do you think the crest moves in one second?

• 340 m
• 172 m
• 85 m

Pick λ and ν

Choose a wavelength and a frequency. The numbers are only examples. Read the speed of the wave.

A wavelength in each period

In one time period T, the crest moves one wavelength. So the speed is v = λ / T. Since ν = 1/T, this gives v = λ × ν.

The speed of sound is the distance a crest or trough travels in unit time. It moves one wavelength in one time period, so v = λ / T = λ × ν (speed = wavelength × frequency).

Notes

The speed of sound is v = λ / T = λ × ν: speed = wavelength × frequency.

Check yourself

A sound wave in air has a frequency of 20 Hz and the speed of sound is 344 m s⁻¹ (as in Example 10.2). What is its wavelength, in m?

Answer: 17.2 m

λ = v ÷ ν = 344 ÷ 20 = 17.2 m.

A wave has a wavelength of 2 m and a frequency of 170 Hz (an example). What is its speed, in m s⁻¹?

Answer: 340 m s⁻¹

v = λ × ν = 2 × 170 = 340 m s⁻¹.

A sound wave in steel has a wavelength of 50 m and the speed of sound in steel is 5000 m s⁻¹ (as in Example 10.4). What is its frequency, in Hz?

Answer: 100 Hz

ν = v ÷ λ = 5000 ÷ 50 = 100 Hz.

In one time period, how far does a crest of a sound wave travel?

• One wavelength — correct. Yes!
• Two wavelengths. In one time period a crest travels one wavelength, so v = λ / T.
• One metre. The crest travels one wavelength in one time period. A wavelength is not always one metre.