Question

Find the minimum and maximum wavelengths of sound in water that is in the audible range (20−20000 Hz) for an average human ear. Speed of sound in water = 1450 m s⁻¹.

Answer 1

Given:
Speed of sound in water v = 1450 ms⁻¹
Audible range for average human ear = (20-20000 Hz)
Relation between frequency (f) and wavelength (λ) with constant velocity:
$f\propto \frac{1}{\lambda }$
(a) For minimum wavelength, the frequency should be maximum.

Frequency f = 20 kHz

$$\begin{gathered} \mathrm{As}v=f\lambda , \\ \therefore \lambda =\frac{v}{f}. \\ \Rightarrow \lambda =\left(\frac{1450}{20\times {10}^3}\right) \\ \Rightarrow \lambda =7.25\mathrm{cm} \end{gathered}$$

(b) For maximum wave length, the frequency should be minimum.

f = 20 Hz
$$\begin{gathered} v=f\lambda \\ \Rightarrow \lambda =\left(\frac{1450}{20}\right)=72.5\mathrm{m} \end{gathered}$$
∴ λ = 72.5 m