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]
Medium
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(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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