Question

A train is moving at 30ms${}^{-1}$ in still air. The frequency of the locomotive whistle is 500 Hz and the speed of sound is 345 ms${}^{-1}$. The apparent wavelengths as heard by stationary listeners in front of and behind the locomotive if a wind of speed 10m/s were blowing in the same direction as that in which the locomotive is travelling is given by

• A. 0.65m, 0.73m
• B. 0.60m, 0.73m
• C. 0.65m, 0.78m
• D. 0.60m, 0.71m

Answer 1

Answer: (A)

0.65m, 0.73m

Velocity of sound will be $v+v_{\omega }$ in the direction and $v-v_{\omega }$ opposite to the direction similarly in front speed will be summed and subtracted behind.
$\therefore f^{\prime }=\left(\frac{v+v_{\omega }+v_t}{v}\right)f$

$\Rightarrow {\lambda }^{\prime }=\left(\frac{v}{v+v_{\omega }+v_t}\right)\lambda$

Similarly behind, it is: ${\lambda }_1^{\prime }=\left(\frac{v}{v-v_{\omega }-v_t}\right)\lambda$

$\therefore {\lambda }^{\prime }=0.65m;{\lambda }_1^{\prime }=0.73m$