Question

A police car moving with velocity $\frac{v_s}{8}$ where $v_s$ is the speed of sound, emits a siren with a frequency of $f$. Calculate the frequency heard by a stationary observer toward whom the car is driving?

• A. $\frac{f}{8}$
• B. $\frac{7f}{8}$
• C. $f$
• D. $\frac{8f}{7}$
• E. $8f$

Answer 1

The correct option is D $\frac{8f}{7}$

Speed of sound $v_{sound}=v_s$

Speed of sound source $v_{source}=\frac{v_s}{8}$

Let the apparent frequency heard by the observer be $f^{\prime }$.

Using Doppler effect in case when the source moves towards the stationary observer :

$\therefore$ $f^{\prime }=f[\frac{v_{sound}}{v_{sound}-v_{source}}]=$ $f[\frac{v_s}{v_s-\frac{v_s}{8}}]=\frac{8f}{7}$