Question

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 $f^{\prime }$ recorded by the observer with time $t$?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

After time $t$, velocity of observer,
$v_0=u+at=at$
[observer starts from rest]
Now, observed frequency,
$f^{\prime }=\left(\frac{v+v_0}{v-v_s}\right)f$
$\Rightarrow f^{\prime }=\left(\frac{v+at}{v}\right)f$
$\Rightarrow f^{\prime }=\left(\frac{af}{v}\right)t+f$
This equation is similar to the equation of straight line, $y=mx+c$,
here,
Slope of straight line, $m=\frac{af}{v}$ and
$y-$intercept, $c=f$.