Question

A sound wave traveling in the air is made to propagate through a liquid such that the velocity of sound is quadrupled. If the frequency of the sound wave is constant, find the change in the wavelength of the sound wave.

Answer 1

Let the speed of sound in air be $v$ and frequency of sound be $f$.

Wavelength of sound in air

${\lambda }_a=\frac{v}{f}$

Speed of sound in liquid

$v_l=4v$

Thus wavelength of sound in liquid

${\lambda }_l=\frac{v_l}{f}$

$\Rightarrow {\lambda }_l=\frac{4v}{f}$

Change in wavelength of sound wave

$\Delta \lambda ={\lambda }_l-{\lambda }_a$

$\therefore$ $\Delta \lambda =\frac{4v}{\nu }-\frac{v}{\nu }$

$\Rightarrow \Delta \lambda =\frac{3v}{\nu }$