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 $350m/s$ then the speed of engine is

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

Answer 1

Answer: (B)

$70m/s$

Apparent pitch heard by the observer $f^{\prime }=\frac{5}{6}f$

where $f$ is the original pitch of the engine.

As the apparent frequency is lowered, thus the engine must be moving away from the stationary observer.

From Doppler effect, apparent frequency heard $f^{\prime }=f[\frac{v_{sound}}{v_{sound}+v_{source}}]$

$\therefore$ $\frac{5}{6}f=f[\frac{350}{350+v_{source}}]$

$⟹$ $v_{source}=70$ $m/s$