The standard frequency of the musical pitch called “middle C” is 261.6 Hz. How fast, in...
The standard frequency of the musical pitch called “middle C” is 261.6 Hz.
How fast, in meters per second, would a source emitting a tone of middle C have to move toward you so that you would hear the pitch C# (C sharp) above middle C, with a frequency of 277.2 Hz? Assume that takes place in air at a high altitude, where the speed of sound is 303 m/s
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Homework Answers
Given,
The standard frequency of "middle C", f = 261.6 Hz
The frequency above middle C, f' = 277.2 Hz
By the Doppler effect, the observed frequency is,
f' = cf / (c - vs)
c - vs = cf / f'
vs = c - (cf / f')
vs = c [1 - (f / f')]
Here, c is the speed of sound = 303 m/s
vs = 303 * [1 - (261.6 / 277.2)]
vs = 17.05 m/s
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