Question

A detector is released from rest over a source of sound of frequency $f_0={10}^3\text{Hz}$. The frequency observed by the detector at time $t$ is plotted in the graph. The speed of sound in air is $(g=10{\text{m/s}}^2)$

• A. $330\text{m/s}$
• B. $350\text{m/s}$
• C. $300\text{m/s}$
• D. $310\text{m/s}$

Answer 1

The correct option is C $300\text{m/s}$

Initially the detector (observer) is at rest.
Velocity of observer after $30\text{sec}$,
$v_0=0+gt=10\times 30=300\text{m/sec}$
Given : $f_0=1000\text{Hz}$ and $f=2000\text{Hz}$ using doppler's effect in case an observer moves towards the stationary source;
$f=f_0\left[\frac{v+v_0}{v}\right]$
(where $v$ is the speed of sound in air)
$\therefore 2000=1000\left[\frac{v+300}{v}\right]$
$\Rightarrow v=300\text{m/sec}$