Question

A boy is standing at a railroad crossing for a track that runs east and west. As he faces the track, east is to his right and west is to his left. Two trains on the track some distance apart are headed west, both at speeds of 8.40 m/s, and blowing their whistles (which have the same frequency). One train is approaching him from the east and the other is traveling away from him toward the west. (Assume the speed of sound is 343 m/s.) (a) If he hears a beat frequency of 6.50 Hz, determine the frequency (in Hz) emitted by the two whistles.

Answer 1

`f_o = 132.91 Hz`

Step-by-step explanation:

Frequency of the train whistle which is approaching him is given as

`f_1 = ((v)/(v - v_s)) f_o`

`f_1 = ((343)/(343 - 8.40)) f_o`

now similarly the frequency of the train whistle which is moving away from him is given as

`f_2 = ((v)/(v + v_s))f_o`

`f_2 = ((343)/(343 + 8.40))f_o`

now we know that

`f_(beat) = f_1 - f_2`

so we have

`6.50 = ((343)/(343 - 8.40)) f_o - ((343)/(343 + 8.40)) f_o`

`6.50 = 1.025 f_o - 0.976 f_o`

`f_o = 132.91 Hz`