Question

A policeman blows a whistle with a frequency of $500Hz$. A car approaches him with a velocity of $15m{s}^{-1}$. The change in frequency as heard by the driver of the car as he passes the policeman is (Given, speed of sound in air is $300m{s}^{-1})$

• A. $25Hz$
• B. $50Hz$
• C. $100Hz$
• D. $150Hz$

Answer 1

Answer: (B)

If the car approaches the policeman
${\upsilon }^{\prime }=\frac{v+v_0}{v-v_s}\times \upsilon$
$=\frac{300+15}{300-0}\times 500$
$\Rightarrow {\upsilon }^{\prime }=525Hz$
If the car moves away from the policeman
${\upsilon }^{\prime \prime }=\frac{v-v_0}{v-v_s}\times \upsilon$
$=\frac{300-15}{300-0}\times 500$
${\upsilon }^{\prime \prime }=475Hz$
Change in frequency $={\upsilon }^{\prime }-{\upsilon }^{\prime \prime }=525-475$
$=50Hz$