Question

The pitch of the whistle of an engine appears to drop to $\left(\frac{5}{6}\right)th$ of original value when it passes a stationary observer. If the speed of sound in air is $350$ m/s then the speed of engine is

• A. 35 m/s
• B. 70 m/s
• C. 105 m/s
• D. 140 m/s

Answer 1

The correct option is B 70 m/s

Given : Speed of sound in air, $v_{sound}=350$ $m/s$

Original frequency of the whistle, $=\nu$

Frequency heard by the stationary observer, ${\nu }^{\prime }=\frac{5}{6}\nu$

Let the speed of the engine be $v$ when it passes a stationary observer.

Using Doppler effect when a sound source moves away from the stationary observer :

The apparent frequency heard by the observer, ${\nu }^{\prime }=\nu [\frac{v_{sound}}{v_{sound}+v}]$

$\Rightarrow \frac{5}{6}\nu =\nu [\frac{350}{350+v}]$

$\Rightarrow v=70$ $m/s$