Question

A source of sound and detector are placed at the same place on ground. At t = 0, the source S is projected towards reflector with velocity $V_0$ in vertically upward direction and reflector starts moving down with constant velocity $v_0$. At t = 0, the vertical separation between the reflector and source is $H(>\frac{v_0^2)}{2g})$. The speed of sound in air is $v(\gg v_0)$. Take f_0 as frequency of sound waves emitted by source. Based on above information answer the following questions.

Wavelength of sound waves as received by detector before reflection at $t=\frac{V_0}{2g}$,is

• A. $\frac{v}{f_0}$
• B. $\frac{v+\frac{v_0}{2}}{f_0}$
• C. $\frac{\{v-\frac{v_0}{2}{\}}^2}{v{f}_0}$
• D. $\frac{v-\frac{v_0}{2}}{f_0}$

Answer 1

The correct option is B $\frac{v+\frac{v_0}{2}}{f_0}$

As the source is initially projected with velocity $v_0$ upwards, the velocity of the source after a time $\frac{v_0}{2g}$ is
$V=V_0-\frac{v_0}{2g}\times g=\frac{v_0}{2}$
And the source is moving away from observer, so,
Frequency heard $=\left(\frac{v}{v+\frac{v_0}{2}}\right)f_0$
So, wavelength of sound $=\frac{v+\frac{v_0}{2}}{f_0}$