Q. A train moves towards a stationary observer with speed$34\ ms^{- 1}$. The train sounds a whistle and its frequency registered by the observer is$v_{1}$. If the train’s speed is reduced to$17\ ms^{- 1}$, the frequency registered is$v_{2}$. If the speed of sound is $340\ ms^{- 1}$, then the ratio $v_{1}/v_{2}$is
A) 2
B) 1/2
C) 18/19
D) 19/18
Explanation
(d) Perceived frequency by observer in Ist case
$v_{1} = v\binom{v}{v - v_{s}}$
$\therefore\ \ \ v_{1} = v\left( \frac{340}{340 - 34} \right) = \frac{340v}{306}$
Perceived frequency by observer in IInd case
$v_{2} = v\left( \frac{340}{340 - 17} \right) = \frac{340v}{323}$
Therefore,
$\frac{v_{1}}{v_{2}} = \frac{340v}{306} \times \frac{323}{340v} = \frac{323}{306} = \frac{19}{18}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.