Question

A train moves towards a stationary observer with speed $34m/s$. The train sounds a whistle and its frequency registered is $f_1$. If the train’s speed is reduced to $17m/s$, the frequency registered is $f_2$. If the speed of sound is $340m/s$ then the ratio $\frac{f_1}{f_2}$ is

• A. $\frac{18}{19}$
• B. $\frac{1}{2}$
• C. $2$
• D. $\frac{19}{18}$

Answer 1

The correct option is D $\frac{19}{18}$

Let $f_0$ be natural frequency of source, then apparent frequency heard by stationary observer is given by
$f=f_0\left[\frac{v}{v-v_s}\right]$

where $v$ is velocity of the sound
$v_s$ is velocity of the source

$\Rightarrow f_1=f_0\left[\frac{v}{v-34}\right],$
$\Rightarrow f_2=f_0\left[\frac{v}{v-17}\right]$

$\Rightarrow \frac{f_1}{f_2}=\left[\frac{v-17}{v-34}\right]=\left[\frac{340-17}{340-34}\right]=\frac{19}{18}$