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 46.3 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. ____Hz

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. ___m

Explanation / Answer

From the Doppler eqn we have fL = fS*(v/(v + vs)) where fL is the listener's frequency; fS is the source frequency v = speed of sound about 343m/s and vs is the velocity of the source (negative if approaching and + if receding)

So for approach fL = 325*(343 /(343 - 46.3)) = 375.7Hz

And for receding fL = 325*(343 /(343 + 46.3)) = 286.3Hz

So the overall change is 375 - 286.3 = 88.7Hz

b) we have v = ?*f ...so

? L1= v/f = 343/375.7 =- 0.912m

? L2=v/f=343/286.3Hz=1.198m

So the overall change is

(- 0.912-1.198m)

? L=-2.11m

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