3(b)
The human ear can detect continuous sounds in the frequency range from 20 Hz to 20,000 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.
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Given,
V = 330 m s-1
fmin = 20 Hz,
fmax = 20,000 Hz
From relation, V = fλ
λmin = $\frac{V}{f_{max}}$ = $\frac{330}{20,000}$ = 1.65 x 10-2 m or 16.5 mm
and
λmax = $\frac{V}{f_{min}}$ = $\frac{330}{20}$ = 16.5 m
Thus, audible range of wavelength is from 16.5 mm to 16.5 m.