The pattern of sound waves emitted by a source traveling at constant velocity is

Question

The pattern of sound waves emitted by a source traveling at constant velocity is shown in the animation below. The source in the animation travels at a speed of 50% of the speed of the waves in the medium. At rest, the source emits a frequency of 660 Hz. The small rectangle in the animation represents an observer. If the source travels toward the observer at a constant velocity of 44.0% of the speed of the waves in the medium, what is the frequency of the waves observed by the observer? After the source passes the observer, what is the frequency of the waves observed by the observer?

Explanation / Answer

Here,

frequency emitted , f0 = 660 Hz

speed of observer , v = (0.44 + 0.50) * vs

vs is the speed of sound

a) when the source is travelling towards oberver

frequency heard = f0 * (vs + v)/vs

frequency heard = 660 * (0.84* vs + vs)/vs

frequency heard = 1214 Hz

the frequency heard when the source is travelling towards oberver is 1214 Hz

b)

when the source is travelling away from oberver

frequency heard = f0 * (-vs + v)/vs

frequency heard = 660 * (-0.06 * vs + vs)/vs

frequency heard = 620.4 Hz

the frequency heard when the source is travelling away oberver is 620.4 Hz

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