You hear the train whistle at 3000 Hz as it comes at you and at 2400 Hz as it mo

Question

You hear the train whistle at 3000 Hz as it comes at you and at 2400 Hz as it moves away. Using only the two frequencies given above, what is the velocity of the train? Use this velocity and one of the frequencies above to determine the frequency of the whistle. What is it? If the whistle on the train was a half pipe and that the sound emitted was at its first overtone, what is the length of the whistle? If the whistle on the train was a pipe open at both ends and that the sound emitted was at its first harmonic, what is the length of the whistle? The whistle on the train wasn't a whistle, but a guitar string of mass 20g and length 1.2meters. If the guitar string was plucked and it was resonating at its fundamental frequency, what is the tension of the string?

Explanation / Answer

v=vel of sound=343.33 vs=vel of source from doppler effect source approaching : f'=v/(v-vs) * f source leaving : f''=v/(v+vs) * f dividing f'/f'' = (v+vs)/(v-vs) so 3000/2400 = (343.33+vs)/(343.33-vs) a)so vs=38.15 m/s (ans) b)so f= f'*(v-vs)/v=2666.67 m/s (ans)

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