Question

A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from $440\, Hz$ to $480 \,Hz ,$ when it gets reflected from the wall. If the speed of sound in air is $345\, m / s ,$ then the speed of the car is

• A. $36\, km / hr$
• B. $24\, km / hr$
• C. $18\, km / hr$
• D. $54\, km / hr$

Answer 1

Answer: (D)

$f _{1}=$ frequency heard by wall
$= f _{ s }=\left(\frac{ v _{ s }}{ v _{ s }- v _{ c }}\right)$
$f _{2}=$ frequency heard by driver after reflection from wall
$f_{2}=\left(\frac{v_{s}+v_{c}}{v_{s}}\right) f_{1}=\left(\frac{v_{s}+v_{c}}{v_{s}-v_{c}}\right) f_{0}$
$\frac{ f _{2}}{ f _{0}}=\frac{ v _{ s }- v _{ c }}{ v _{ s }+ v _{ c }}$
$\frac{48}{44}=\frac{v_{s}-v_{c}}{v_{s}+v_{c}}$
$12\left( v _{ s }+ v _{ c }\right)=11\left( v _{ s }- v _{ c }\right)$
$23 v_{c}=v_{s}$
$v _{ c }=\frac{ v _{ s }}{23}=\frac{345}{23}=15 m / s$
$=\frac{15 \times 18}{5}=54 km / hr$