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 $y=c+mx$
Where $c=-\frac{f_{0}v}{v-v_s}$ and slope $(m)=\frac{f_0}{v-v_s}$