Question

A siren producing a sound of frequency $750\text{Hz}$ moves away from an observer at rest towards a cliff at a speed of $30\text{m/s}$. The frequency of echo heard by the observer reflected from the cliff is
[speed of sound in air $=330\text{m/s})$

• A. $800\text{Hz}$
• B. $750\text{Hz}$
• C. $775\text{Hz}$
• D. $825\text{Hz}$

Answer 1

The correct option is D $825\text{Hz}$


From Doppler's effect, the apparent frequency heard by the observer is,
$f^{{}^{\prime }}=f_0\left(\frac{v\pm v_0}{v\pm v_s}\right)$, here,
$f_0$ is the original frequency produced by the source, $v$ is the speed of sound, $v_0$ is the speed of observer and $v_s$ is the speed of source.
The frequency received by cliff
$\Rightarrow f^{{}^{\prime }}=750\times \left(\frac{330+0}{330-30}\right)$
[as separation is decreasing, so frequency will increase]
$\Rightarrow f^{{}^{\prime }}=825\text{Hz}$
This is the frequency which the cliff will reflect.
And as the observer is at rest, so it will hear the echo of the same frequency.
Hence, the frequency of echo heard by the observer reflected from the cliff is $825\text{Hz}$.