Question

A train on one track moves in the same direction as a second train on the adjacent track. The first train, which is ahead of the second train and moves with a speed of 36.4 m/s, blows a horn whose frequency is 123 Hz. Part A If the frequency heard on the second train is 134 Hz , what is its speed?

Answer 1

Let the speed of sound in air, v = 340 m/s

This is the case of Doppler effect when both source and observer are moving along the same direction. Here, first train is the source moving with, v_s = 36.4 m/s and second train is the observer moving with velocity v_o.

Apparent frequency, f' = 134 Hz

Actual frequency, f = 123 Hz

So, by formula,

   $f'= (\frac{v+v_o}{v+v_s})f$

Thus, 134 = 123*{(340+v_o)/(340+36.4)}

Or, 134*376.4/123 = 340+v_o

Or, 410.06 = 340 + v_o

Thus, velocity of second train = (410.06-340) m/s

= 70.06 m/s