Question

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

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

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
$f_2=\left(\frac{v_s+v_c}{v_s}\right)f_1=\left(\frac{v_s+v_c}{v_s-v_c}\right)f_0$
$\frac{f_2}{f_0}=\frac{v_s-v_c}{v_s+v_c}$
$\frac{48}{44}=\frac{v_s-v_c}{v_s+v_c}$
$12\left(v_s+v_c\right)=11\left(v_s-v_c\right)$
$23v_c=v_s$
$v_c=\frac{v_s}{23}=\frac{345}{23}=15m/s$
$=\frac{15\times 18}{5}=54km/hr$