Question

If the wavelength of sound in air incident on reflecting surface is $\frac{x}{10}m$. Find $x$.

Answer 1

Let the wavelength of the incident wave on the reflecting surface be ${\lambda }^{\prime }.$

For the incident wave, assume the observer (refleccting surface ) be at rest and source is moving towards the observer with $v_{source}=32m/s$

Using Doppler effect when source is moving and observer is at rest:

${\nu }^{\prime }=\nu [\frac{v_{sound}}{v_{sound}-v_{source}}]$

${\nu }^{\prime }=1000[\frac{332}{332-32}]$ $=1000[\frac{332}{330}]$

Now, $v_{sound}={\nu }^{\prime }{\lambda }^{\prime }$

$332=1000\times \frac{332}{300}\times {\lambda }^{\prime }⟹{\lambda }^{\prime }=\frac{3}{10}$

Thus $x=3$