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.
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
`323 = (340/(340-v))f0------(1)`
When car recedes
`278 = (340/(340+v))f0-----(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`