Question

A car is moving towards a person. the person observes a change of 2.5% in the frequency of its horn. If the velocity of sound is 320 m$s^{-1}$, then the velocity of the car is :

• A. 6 m$s^{-1}$
• B. 8 m$s^{-1}$
• C. 7.5 m$s^{-1}$
• D. 800 m$s^{-1}$

Answer 1

Answer: (B)

8 m$s^{-1}$

Let the original frequency of the car be $f_o$.
Since the car is moving towards the stationary observer, so the apparent frequency heard by the observer is greater than original frequency.
Apparent frequency heard $f=1.025f_o$
Using Doppler effect,
$f=f_o[\frac{V_{sound}}{V_{sound}-V_{car}}]$
$\therefore$ $1.025f_o=f_o[\frac{320}{320-V_{car}}]$
$⟹V_{car}=8m/s$