Question

In a car race sound signals emitted by the two cars are detected by the detector on the straight track at the end point of the race. Frequency observed are 330 Hz & 360 Hz and the original frequency is 300 Hz of both cars. Race ends with the separation of 100 m between the cars. Assume both cars move with constant velocity and velocity of sound is 330 m/s. Find the tiime taken by winning car (in sec.)

Answer 1

Let the velocities of car 1 and car 2 be $V_{1}m/sand{V}_{2}m/s.$
$\therefore$ Apparent frequencies of sound emitted by car 1 and car 2 as detected at end point are $f_1=f_0\frac{V}{V-V_1},f_2=f_0\frac{V}{V-V_2}$
$\Rightarrow 330=300\frac{330}{330-V_1},360=300\frac{330}{330-V_2}$
$\Rightarrow V_1=30m/sand{V}_2=55m/s.$
The distance between both the cars just when the 2nd car reach end point.

$100m=V_{2}t-V_{1}t\Rightarrow t=4sec$.