Question

A car is parked on the side of the road with the radio playing. Physics students in the car measure the sound coming from the radio to be 18.2 kHz. Another physics student is riding a bike and moving towards the car at 30 km/h.

a) What is the frequency of the radio as heard by the physics student riding the bike?

b) The physics student riding the bike passes the car and starts to move away from the car. What now, is the frequency of the radio as heard by the physics student riding the bike?

Please help me with this.

Answer 1

Let,

• : be the frequency measured by the physics student in the car.
• : be the frequency heard by the physics student riding the bike when moving toward the car.
• : be the frequency heard by the physics student riding the bike when moving away from the car.
•    : be the speed of the sound.
• : be the speed of the bike.

Given:-

• 
• 
• 

We will use Doppler effect to find out the frequency heard by the moving observer i.e. physics student on a bike.

In this question, the car is a source of sound and physics student on a bike is a observer. And note that in both cases, the source is stationary.

Part (a)

In this case the physics student is moving towards the car. The car becomes source, which is stationary, and the physics student here becomes the observer.

Thus the apparent frequency change is given by,

This is the frequency of the radio as heard by the physics student riding the bike when moving towards the car.

Part (b)

In this case the physics student is moving away from the car as he passes the car. Thus the apparent frequency change is given by,

This is the frequency of the radio as heard by the physics student riding the bike when moving away from the car.