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 437 Hz and a passenger in the front hears it at 412 Hz. Find the train's speed and the horn's frequency, assuming the sound travels along the tracks. Take the speed of sound to be 343 m/s.

(a) the train's speed (in m/s)

m/s

(b) the horn's frequency (in Hz)

Hz

Explanation / Answer

for the front passenger

apparant frequency is f'= (V*f)/(V+Vs)

412 = (343*f)/(343+Vs)

343*f = 412*(343+Vs)................(1)

for the back passenger

apparant frequency is f' = (V*f)/(V-Vs)

437 = (343*f)/(343-Vs)

343*f = 437*(343-Vs)............(2)

from (1) and (2)

412*(343+Vs) = 437*(343-Vs)

solving we get
Vs = 10.1 m/sec

b) horn;s frequency is f

343*f = 437*(343-Vs)

343*f = 437*(343-10.1)

f = 424.13 Hz

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.