Question

A source of sound emits sound waves at frequency $f_0$. It is moving towards an observer with fixed speed $v_{s} (v _{s}< v ,$, where $v$ is the speed of sound in air). If the observer were to move towards the source with speed $v_{0}$ one of the following two graphs (A and B) will give the correct variation of the frequency $f$ heard by the observer as $v_{0}$ is changed.
The variation of $f$ with $v_{0}$ is given correctly by

• A. graph A with slope $=\frac{f_{0}}{\left(v-v_{s}\right)}$
• B. graph A with slope $=\frac{f_{0}}{\left(v+v_{s}\right)}$
• C. graph B with slope $=\frac{f_{0}}{\left(v-v_{s}\right)}$
• D. graph B with slope $=\frac{f_{0}}{\left(v+v_{s}\right)}$

Answer 1

Answer: (A)

$f=f_{0}\left(\frac{v +v_{0}}{v +v_{s}}\right)$ by Doppler's effect in sound
$=\frac{f_{0} v}{v-v_{s}}+\frac{f_{0} v_{0}}{v-v_{s}}$ resembles $y=c+ m x$
Where $c=-\frac{f_{0} v}{v-v_{s}}$ and slope $(m)=\frac{f_{0}}{v-v_{ s }}$