A railroad train is traveling at 31.0 m/s in still air. The frequency of the not

Question

A railroad train is traveling at 31.0 m/s in still air. The frequency of the note emitted by the locomotive whistle is 500 Hz. (Assume the speed of sound in air is 344 m/s.) (a) What is the wavelength of the sound waves in front of the locomotive? m (b) What is the wavelength of the sound waves behind the locomotive? m (c) What is the frequency of the sound heard by a stationary listener in front of the locomotive? Hz (d) What is the frequency of the sound heard by a stationary listener behind the locomotive? Hz

Explanation / Answer

let,

object speed, vo=31 /sec

frequency of the source, fs=500 Hz

velocity of the sound, vs=344m/sec

a)

frquency in front of the train,

fo=fs*(vs/(vs-vo))

fo=500*(344/(344-31))

fo=549.52 Hz

and

wavelength, lambda=vs/fo

=344/(549.52)

=0.626 m

b)

frquency behind the train,

fo=fs*(vs/(vs+vo))

fo=500*(344/(344+31))

fo=458.66 Hz

and

wavelength, lambda=vs/fo

=344/(458.66)

=0.75 m

c)

fo=549.52 Hz

d)

fo=458.66 Hz

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