The human ear can detect continuous sounds in the frequency range from 20 Hz to 20000 Hz. Assuming that the speed of sound in air is 330 ms-1 for all frequencies, calculate the wavelengths corresponding to the given extreme frequencies of the audible range
Topic: Sound and vibrations
Answer
Given: v = 330 m s⁻¹, frequency range 20 Hz to 20 000 Hz
The wave equation is v = f λ, so λ = v ÷ f.
At the lower limit, f = 20 Hz: λ = 330 ÷ 20 = 16.5 m
At the upper limit, f = 20 000 Hz: λ = 330 ÷ 20 000 = 0.0165 m = 1.65 cm
The wavelengths range from 16.5 m (at 20 Hz) down to 0.0165 m (at 20 000 Hz).
One formula, used twice. The only care needed is keeping track of which frequency goes with which wavelength.
Frequency and wavelength are INVERSELY related at a fixed speed: the lowest frequency gives the LONGEST wavelength. If your 20 Hz answer came out smaller than your 20 000 Hz answer, you have divided the wrong way round. A thousand-fold rise in frequency gives a thousand-fold fall in wavelength — 16.5 m to 0.0165 m — which is a quick way to check the second answer once you have the first.