As a race car approaches a fan in the stand the fan hears the noise of the engine 323Hz. As the car recedes he hears the noise at 278Hz.If speed of sound in air is 343m/s calculate the speed of car.

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

This is related to Doppler effect. By this it analyses the frequency or wave received for an stationary observer relative to a moving source.

The equation is given as follows.

`f = (c/(c+v))f0`

f = observed frequency

c = velocity of the waves in the medium

v = velocity of the source relative to medium.(if source approach observer v is negative and if it moves away v is positive.)

For our question medium is air. The waves are the sound. Therefore c = 340m/s

f0 is the frequency of noise when the object doesn't move.

When car approaching

`f =(c/(c-v))f0`

`323 = (340/(340-v))f0------(1)`

When car recedes

`f =(c/(c-v))f0`

`278 = (340/(340+v))f0-----(2)`

`(1)/(2)`

`323/278 = [(340/(340-v))f0]/[(340/(340+v))f0]`

`323/278 = (340+v)/(340-v)`

`323(340-v) = 278(340+v)`

`340(323-278) = v(278+323)`

`v = (340*45)/601`

`v = 25.46`

So the velocity of the car is `25.46m/s`

Sources: