A train is moving past a crossing where cars are waiting for it to pass. While waiting, the driver of the lead car becomes sleepy and rests his head on the steering wheel, unintentionally activating the car's horn. A passenger in the back of the train hears the horn's sound at a frequency of 428 Hz and a passenger in the front hears it at 402 Hz. Find the train's speed and the horn's frequency. Take the speed of sound to be 343 m/s.

Question

(a) the trains speed (in m/s)

(b) the horns frequency (in Hz)

Answer 1

Google Doppler effect
f = fo (c +/- Vr ) / (c +/- Vs )fo = real frequency
c = speed of signal
Vr = 0 here ( receiver not moving)
Vs = + when toward, - when away
so
402 = fo (343)/ ( 343 + Vs)
428 = fo (343)/ ( 343 - Vs )

Answer 2

b. Fg = (402+428)/2 = 415 Hz. = Generator(horn) freq.

a. Fr = (Vs+Vr)/(Vs+Vg) * Fg = 428.
(343+Vr)/(343+0) * 415 = 428,
(343+Vr) * 415 = 146,804,
343+Vr = 353.7,
Vr = 10.7 m/s. = Velocity of receiver(train).

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