Question

The speed at which a source of sound should move so that a stationary observer finds the apparent frequency equal to half of the original frequency

• A. $\frac{V}{2}$
• B. $2V$
• C. $\frac{V}{4}$
• D. $V$

Answer 1

The correct option is D $V$

$\vartheta =Vm/s$
Given : ${\vartheta }_0=Om/s$ and $f^{\prime }=\frac{8}{2}$

By doppler effect formula:
$f^{\prime }=f\left(\frac{\vartheta -{\vartheta }_0}{\vartheta -{\vartheta }_s}\right)$

$\Rightarrow \frac{f}{2}=f\left(\frac{\vartheta -o}{V-{\vartheta }_s}\right)$

$\Rightarrow \frac{1}{2}=\frac{V}{V-{\vartheta }_s}$

$\Rightarrow V-{\vartheta }_s=2V$

$\Rightarrow {\vartheta }_s=-V$

So, speed of source should be $V$ away from the observer.