In one of the original Doppler experiments, a tuba was played at a frequency of 75 Hz on a moving flat train car, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard in the station if the train car approached the station at a speed of 14.0 m/s?
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This is Giancoli Answers with Mr. Dychko. The frequency of the tuba which is on the train coming towards the platform will be the frequency emitted by the tuba according to somebody playing the tuba, 75 hertz, divided by 1 minus speed of the source divided by speed of sound. So, this is the formula for a stationary observer on the platform perceiving a frequency from a sound source moving towards them. And the beat frequency that a person on the platform will perceive is this f prime coming from the tuba moving towards them minus the frequency of the tuba that's being played on the platform. And so we can substitute for f prime as f over 1 minus v source over v sound minus f. And that frequency can be factored out. So, the beat frequency will be f times 1 over 1 minus v source over v sound minus 1. So, 75 hertz times 1 over 1 minus 14 over 343 meters per second minus 1 which is about 3.2 hertz for the beat frequency.
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