A train blowing its whistle moves with constant speed on a straig… - Vidyadip

MCQ

A train blowing its whistle moves with constant speed on a straight track towards observer and then crosses him. If the ratio of difference between the actual and apparent frequencies be $3: 2$ in the two cases, then the speed of train is [ $v$ is speed of sound]

A
$\frac{2 v}{3}$
✓
$\frac{v}{5}$
C
$\frac{v}{3}$
D
$\frac{3 v}{2}$

✓

Answer

Correct option: B.

$\frac{v}{5}$

b
(b)

$f_A=\frac{v}{v-v_s} f_0 \quad$ (Frequency of approach)

$f_R=\frac{v}{v+v_s} f_0 \quad$ (Frequency of departing)

$\Delta f_A=\left(\frac{v}{v-v_s}-1\right) f_0$

$\Delta f_A=\frac{v}{v-v_s} f_0$

$\Delta f_R=\left(1-\frac{v}{v+v_s}\right) f_0$

$\Delta f_R=\frac{v}{v+v_s} f_0$

$\frac{\Delta f_A}{\Delta f_R}=\frac{v+v_s}{v-v_s}=\frac{3}{2}$

$2 v=2 v_s=3 v-3 v_s$

$5 v_s=v$

$v_s=\frac{v}{5}$

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