A source of sound emits sound waves at frequency $f_{0}$ . It is moving towards an observer with fixed speed $v_{s} (v_{s} < v$ , where v is the speed of sound in air). If the observer were to move towards the source with speed $v_{0}$ , one of the following two graphs (A and B) will give the correct variation of the frequency f heard by the observer as $v_{0}$ is changed.
The variation of f with $v_{0}$ is given correctly by :

graph A with slope

= \frac{f_{0}}{(v - v_{s})}

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graph A with slope

= \frac{f_{0}}{(v + v_{s})}

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graph B with slope

= \frac{f_{0}}{(v - v_{s})}

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graph B with slope

= \frac{f_{0}}{(v + v_{s})}

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Solution

The correct option is A graph A with slope $= \frac{f_{0}}{(v - v_{s})}$
$f = f_{0} (\frac{v + v_{0}}{v - v_{s}}) = \frac{f_{0}}{v - v_{s}} v_{0} + \frac{f_{0} v}{v - v_{s}}$ where v is velocity of sound
As we see, this is of the form $y = m x + c$
slope m is: $\frac{f_{0}}{v - v_{s}}$

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Similar questions

Q. A source of sound emits sound waves at frequency

f_{0}

. It is moving towards an observer with fixed speed

v_{s}

(

v_{s} < v

, where v is the speed of sound in air). If the observer were to move towards the source with speed

v_{0}

, one of the following two graphs (A and B) will give the correct variation of the frequency f heard by the observer as

v_{0}

is changed.

The variation of f with

v_{0}

is given correctly by:

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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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