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

Answer 1

The correct option is C

$54km/hr$

Step 1: Given Data

Frequency of horn,$f_s=440Hz$

Speed of sound, $v=335m/s$

Frequency of observed sound, $f_o=480Hz$

Step 2: Find the speed of car

According to Doppler effect, Frequency heard by observer is,

$\begin{array}{rcl}{f}_o& =& f_s\frac{v+v_o}{v-v_o}\\ 480& =& 440\frac{335+v_c}{335-v_c}\\ v_c& =& 15m/s\\ v_c& =& 54km/h\end{array}$

Hence, option C is correct.