Question

Youare on a train travelling northat 80.0m/s relative to the ground. The air is still relativetothegroundwhen you hear the whistle of atraintravellingsouth. You know that train whistles are emitted with a frequency of 262Hz, but the whistle appears to have a frequency of 350Hz. What is the speed of the other train?

Answer 1

To solve this problem we will apply the concepts related to the Doppler effect. This is understood as the change in apparent frequency of a wave produced by the relative movement of the source with respect to its observer. Mathematically this is given as,

$f = \frac{v \pm v_r}{v \pm v_s}(f_0)$

Here,

v = Speed of the waves in the middle

$v_r$ = Speed of the receiver in relation to the medium (Positive if the receiver is moving towards the transmitter or vice versa)

$v_s$ = Speed of the source with respect to the medium (Positive if the source moves away from the receiver or vice versa)

Our values are given as,

$v = 342m/s$

$f_0 = 262Hz$

$v_r = 80m/s$

$f = 350Hz$

Replacing,

$350 = \frac{342+80}{342-v} (262)$

Solving for the velocity of the source,

$v = 26.1m/s$

Therefore the speed of the other train is 26.1m/s