Question 158: Waves

Question

A sound source S is moving along a straight track with speed v, and is emitting, sound of frequency
v0
 (see figure). An observer is standing at a finite distance, at the point O, from the track. The
time variation of frequency heard by the observer is best represented by: (t0
 represents the
instant when the distance between the source and observer is minimum)

Accepted Answer

While approaching
v = $${v_0}\left( {{c \over {c - v\cos 	heta }}} ight)$$
While receding
v = $${v_0}\left( {{c \over {c + v\cos 	heta }}} ight)$$
When source is approaching towards observer then $$	heta $$ is inceasing so cos$$	heta $$ is decreasing. As cos$$	heta $$ is decreasing so c - vcos$$	heta $$ is increasing. Then v will decrease.
When source is receding from observer then $$	heta $$ is decreasing so cos$$	heta $$ is increasing. As cos$$	heta $$ is increasing so c + vcos$$	heta $$ is increasing. Then v will also decrease.
As v is changing depending on cos$$	heta $$, so curve should look like cos$$	heta $$ curve.

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Waves

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