You are at a railroad crossing waiting for a freight train traveling at a speed

Question

You are at a railroad crossing waiting for a freight train traveling at a speed of 35.8 m/s to pass by. The frequency of the train's horn is 325 Hz. (Use 343 m/s as the speed of sound.)

(a) Determine the overall change in frequency you detect as the train moves from approaching to receding. Use the sign of your answer to indicate whether the frequency increases or decreases.

(b) Determine the overall change in wavelength you detect as the train moves from approaching to receding. Use the sign of your answer to indicate whether the wavelength increases or decreases.

Explanation / Answer

a)

here

As train approaches, f1 = f*[ u / (u - v )]

f1 = 325 * [343 / (343 - 35.8)] = 362.84 Hz

As train recedes,

f2 = 325 * [343 / (343 + 35.8 )] = 294.28 Hz

Overall df = 294.28 - 362.84 = -68.56 Hz

b)

As train approaches lambda1 = v / f1

lambda1 = 343 / 362.84 = 0.945 m

then

train receding lambda2 = v / f2

lambda2 = 343 / 294.28 = 1.165 m

overall change = 1.165 - 0.945 = 0.22 m

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