A car travelling at 20m/s blows its horn which has a frequency of 600Hz. A stationary observer notices that the frequency of the horn changes considerably as the car passes by him. Calculate the change in frequency heard by the observer as the car approaches and moves away from the observer.(Given velocity of sound =330m/s)

Since the sound of horn is emitted from car, the car can be assumed as the source. So in the present case, the source is moving and the observer is at stationary state. Since the source is moving , the frequency of sound herd by the observer will differ due to doppler effect.

The frequency due to doppler shift can be calculated using the below formula:

[tex]f'=f(\frac{c-v_{o} }{c-v_{s}})[/tex]

Here, f is the original frequency and f' is the doppler shift frequency, c is the speed of sound, while v₀ and vs are the speed for observer and source relative to the medium.

As here the observer is stationary so the speed of observer will be zero, then the doppler frequency formula will be [tex]f'=f(\frac{c }{c-v_{s}})[/tex]

The speed of the source will be added to speed of sound if the source is moving away from the observer and subtracted from speed of sound if the source is coming towards observer.

So in the first case, as the car approaches the observer, the frequency will be

[tex]f'=600*(\frac{330 }{330-20})\\f'=600*(\frac{330 }{310})=639 Hz[/tex]

Then when the car moves away from the observer then the frequency will be

[tex]f'=600*(\frac{330 }{330+20})\\f'=600*(\frac{330 }{350})=566 Hz[/tex]

So, the frequency of the horn sound heard by the observer will be 639 Hz when the car is approaching the observer. And the frequency will be 566 Hz when the car moves away from the observer.