Question

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

Answer 1

Step 1. Given data

Speed of sound $V=1450\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$sec$}\right.$

Maximum frequency $f_{max}=20kHz$

Minimum frequency $f_{min}=20Hz$

Step 2. Calculate minimum wavelength.

For minimum wavelength, frequency should be maximum.

We know, $\lambda =\frac{v}{f_{max}}$

Where $\lambda$ is the wavelength

$V$ is the speed of sound

$f_{max}$ is the Maximum frequency

Therefore, $\lambda =\frac{1450}{20\times {10}^3}=7.25cm$

Step 3. Calculate maximum wavelength.

For maximum wavelength, frequency should be minimum.

We know, $\lambda =\frac{v}{f_{min}}$

Where $\lambda$ is the wavelength

$V$ is the speed of sound

$f_{min}$ is the Minimum frequency

Therefore, $\lambda =\frac{1450}{20}=72.5cm$

Hence, the minimum and maximum wavelengths of sound in water is $7.25cm$ and $72.5cm$respectively.