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Standard XII

Physics

Apparent Frequency:Listener Moving

Starting from...

Question

Starting from rest, an observer moves with a constant acceleration a towards a stationary source emitting a sound of frequency $v_{0}$ . Which of the graphs shown in Fig. correctly represents the variation of the apparent frequency v of sound as heard by the observer with time t?

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Solution

The correct option is D

Speed of observer at time t is $u_{0} = 0 + a t = a t$

Apparent frequency $v = v_{0} (\frac{c + u_{0}}{c})$

$= v_{0} (\frac{c + a t}{c})$

$= v_{0} + \frac{a v_{0}}{c} t$

This is the equation of a straight line with a positive slope $m = \frac{a v_{0}}{v}$ and a positive intercept $c = v_{0}$ .

Hence the correct choice is (d).

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Starting from rest, an observer moves with a constant acceleration a towards a stationary source emitting a sound of frequency v0. Which of the graphs shown in Fig. correctly represents the variation of the apparent frequency v of sound as heard by the observer with time t?

The correct option is D Speed of observer at time t is u0=0+at=at Apparent frequency v=v0(c+u0c) =v0(c+atc) =v0+av0ct This is the equation of a straight line with a positive slope m=av0v and a positive intercept c=v0. Hence the correct choice is (d).

Starting from rest, an observer moves with a constant acceleration a towards a stationary source emitting a sound of frequency $v_{0}$ . Which of the graphs shown in Fig. correctly represents the variation of the apparent frequency v of sound as heard by the observer with time t?