A train is moving past a crossing where cars are waiting for it to pass. While w

Question

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 427 Hz and a passenger in the front hears it at407 Hz. Find the train's speed and the horn's frequency. Take the speed of sound to be 343 m/s.

HINT

(a)

the train's speed (in m/s)

(b)

the horn's frequency (in Hz)

Explanation / Answer

f = f0 ( v + v_r) /(v + v_s)

for back passenger,

v_r = 0

v_s = - vt { v = 343 m/s }

427 = f0 (343 / 343 - vt) ..... (i)

for front, v_S = vt

407 = f0 (343)/(343 + vt) .... (ii)

(i)/(ii) =>

427 / 407 = (343 + vt)/(343 - vt)

359.855 - 1.049 vt = 343 + vt

vt = 8.23 m/s .....Ans (a)

(b) putting in (a)

427 = (343 f0) / (343 - 8.23)

f0 = 416.8 Hz

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