A source of sound producing sound of frequency $f$ is at rest. An observer starts moving toward it at $t = 0$ with a constant small acceleration. Which of the following graph best represents the variation of observed frequency $f^{'}$ recorded by the observer with time $t$ ?

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Solution

The correct option is A
After time $t$ , velocity of observer,
$v_{0} = u + a t = a t$
[observer starts from rest]
Now, observed frequency,
$f^{'} = (\frac{v + v_{0}}{v - v_{s}}) f$
$\Rightarrow f^{'} = (\frac{v + a t}{v}) f$
$\Rightarrow f^{'} = (\frac{a f}{v}) t + f$
This equation is similar to the equation of straight line, $y = m x + c$ ,
here,
Slope of straight line, $m = \frac{a f}{v}$ and
$y -$ intercept, $c = f$ .

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