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)

$50Hz$

If the car approaches the policeman
${\upsilon }^{\prime }=\frac{\nu -{\nu }_0}{\nu -{\nu }_s}\times \upsilon =\frac{300-\left(15\right)}{300-0}\times 500⟹{\upsilon }^{\prime }=525Hz$
If the car moves away from the policeman
${\upsilon }^{\prime \prime }=\frac{\nu -{\nu }_0}{\nu -{\nu }_S}\times \upsilon =\frac{300-15}{300-0}\times 500Hz$
${\upsilon }^{\prime \prime }=475Hz$
Change in frequency $={\upsilon }^{\prime }-{\upsilon }^{\prime \prime }=525-475=50Hz$