Question

A girl is standing at a railroad crossing for a track that runs east and west. As she faces the track, east is to her right and west is to her left. Two trains on the track some distance apart are headed west, both at speeds of 7.20 m/s, and blowing their whistles (which have the same frequency). One train is approaching her from the east and the other is traveling away from her toward the west. (Assume the speed of sound is 343 m/s.)

(a) If she hears a beat frequency of 8.50 Hz, determine the frequency (in Hz) emitted by the two whistles.

(b) What If? What would be the frequency (in Hz) of the beats that she hears if the lead train stops at a station (and continues to blow its whistle) while the second train continues traveling toward her?

Answer 1

a)

from doppler effect of sound

frequency of train coming from east

f1 = fo*v/(v - vt)

frequency of train going away to west

f2 = fo*v/(v + vt)

beat frequency = f1 - f2

beat frequency = fo*v( 1/ (v - vt) - 1/ (v + vt) ) = 8.5

fo*343* ( 1/(343-7.2) - 1/(343+7.2) ) = 8.5

frequency fo = 202.37 hz   <<<--------------answer

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(b)

if trains stops at station

f2 = fo

beat frequency = f1 - f2

beat frequency = fo*v/ (v - vt) - fo

beat frequency = 202.37*343/ (343-7.2) - 202.37 = 4.34 Hz   <<<--------------answer