Question

As you stand near a railroad track, a train passes by at a speed of 31.7 m/s while sounding its horn at a frequency of 218 Hz. What frequency do you hear as the train approaches you and what frequency while it recedes?

Answer 1

Explanation:

Given that,

Frequency of train horn, f = 218 Hz

Speed of train, $v_t = 31.7 m/s$

The speed of sound, V = 344 m/s (say)

The speed of the observed person, $V_o=0\ m/s$

(a) When the train approaches you, the Doppler's effect gives the frequency as follows :

$f'=f(\dfrac{V}{V-v_t})\\\\f'=218\times (\dfrac{344}{344-31.7})\\\\f'=240.12\ Hz$

(b) When the train moves away from you, the Doppler's effect gives the frequency as follows :

$f'=f(\dfrac{V}{V+v_t})\\\\f'=218\times (\dfrac{344}{344+31.7})\\\\f'=199.6\ Hz$

Hence, this is the required solution.