Question

An observer starts moving with uniform acceleration, towards a stationary sound source of frequency $f_{0}$ . As the observer approaches the source, the apparent frequency $\left(f\right)$ heard by the observer varies with time ( $t$ ) is

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

Let $v$ be the speed of sound in air, $v_{L}$ velocity of observer at time t. As the observer approaches the source, therefore, apparent frequency
$f=\frac{\left(\right. v + v_{L} \left.\right)}{v}f_{0}=\left[\frac{v + \left(\right. 0 + a t \left.\right)}{v}\right]f_{0}=f_{0}+\left(\frac{f_{0} a t}{v}\right)$
This is the equation of a straight line with a positive intercept $\left(f_{0}\right)$ and positive slope $\left(\frac{f_{0} a}{v}\right)$ .