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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.
Solution
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
\[\text { As } v = f\lambda, \]
(b) For maximum wave length, the frequency should be minimum.
f = 20 Hz
\[v = f\lambda\]
\[ \Rightarrow \lambda = \left( \frac{1450}{20} \right) = 72 . 5 \text { m }\]
∴ λ = 72.5 m
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