Question

A car iS moving towards a fixed wall. It blows horn of frequency of 440 Hz. The frequency of reflected sound observed by the driver is 480 Hz then find the speed of car in km/hw. (Speed of sound is 350 m/sec) :

Answer 1

It has given that, A car moving towards a fixed wall blows horn of frequency of 440 Hz. The frequency of reflected sound observed by the driver is 480 Hz.

To find : the speed of car in km/h. (speed of sound is 350 m/s)

solution : using Doppler's effect,

$f=f_0\left(\frac{v_s+v_c}{v_s-v_c}\right)$

where $f_0$ is frequency of horn of car.

$v_s$ speed of sound

$v_c$ speed of car

f is frequency observed by the driver.

here, $f_0$ = 440 Hz, $v_s$ = 350 m/s ,and f = 480 Hz

so, 480 = 440(350 + v_c)/(350 - v_c)

⇒12/11 = (350 + v_c)/(350 - v_c)

⇒12 × 350 - 12v_c = 11 × 350 + 11v_c

⇒350 = 23v_c

⇒v_c = 350/23 m/s = 350/23 × 18/5 = 1260/23

= 54.78 km/h

Therefore the speed of car is 54.78 km/h