Answer to Question #161991 in Optics for Onel

Question

A train whistle ( f = 400Hz ) sounds higher or lower in frequency depending on whether it approaches or recedes. Calculate this difference for a train moving at a speed of 130km/h . Take the speed of sound in air to be 340m/s

Answer 1

Answer

f=400Hz

V=130Km/hr=36m/s

$V_s=340m/s$

When it goes towards to stationery observer

$f_a=f(\frac{V}{V-V_s}) =400(\frac{340}{340-36}) \\=447.4Hz$

Now when it's away from stationary obserser

$f_a'=f(\frac{V}{V+V_s}) =400(\frac{340}{340+36})\\ =361.7Hz$

Now frequency difference

$\Delta f=f_a-f_a'=447.4-361.7\\=85.7Hz$