Question

Two passenger trains moving with a speed of $108km/\text{hour}$ cross each other. One of them blows a whistle whose frequency is $750Hz$. If sound speed is $330m/s$., then passengers sitting in the other train, after trains cross each other will hear sound whose frequency (in $Hz$.) will be

Answer 1

Formula Used: $n^{\prime }=n\left(\frac{v-v_0}{v+v_s}\right)$


Given, speed of the passenger train,
$v_s=108\frac{km}{hr}$

$=108\times \frac{5}{18}=30m/s$

Actual frequency of the whistle, $n=750Hz$
Speed of the observer,

$v_0=108\frac{km}{hr}=108\times \frac{5}{18}=30m/s$

Speed of the sound, $v=330m/s$

Now the passengers sitting in the other train, after trains cross each other will hear sound frequency,

$\Rightarrow n^{\prime }=n\left(\frac{v-v_0}{v+v_s}\right)$

$\Rightarrow n^{\prime }=750\left(\frac{330-30}{330+30}\right)$

$\Rightarrow n^{\prime }=750\left(\frac{300}{360}\right)$

$\Rightarrow n^{\prime }=625Hz$

Final answer: 625 Hz