### Special Relativity

## Doppler Effect with Photons

### introduction

The Doppler effect was first proposed by Doppler in 1856 to explain the apparent change in pitch of a source of sound as it moves. The faster it moves the greater the effect. The same is also true for a source of light with the change in pitch of the light resulting in a change of colour.

There is a relativistic component to the Doppler effect which is significant at high velocities. This relativist component is always smaller than the classical Doppler effect, but is important later in the course when we consider the derivation of E = mc^{2}.

### animation

The animation is a view of two identical spacecraft emitting photons at regular intervals. Both spacecraft emit two photons every second as regulated by an onboard clock. One photon is emitted out the front and the other is emitted out the back of the spacecraft. The bottom spacecraft is stationary relative to you. The speed of the top spacecraft can be set with the buttons under the animation.

When the speed of the spacecraft is set to anything other than zero then the Doppler effect becomes apparent. An observer recording the frequency of the photons emitted out the front of the moving spacecraft will notice that they arrive more frequently than once every 1 second. An observer recording the frequency of the photons emitted out the back of the moving spacecraft will notice that they arrive less frequently than once every 1 second.

The relativistic component is as a consequence of time dilation. The moving light bulb flashes less frequently than once every second due to time dilation. The relativistic effect causes an overall decrease in the frequency compared to the classical Doppler effect.

Try selecting a speed of 0.866c. You will notice that moving light bulb flashes at half the rate of the stationary light bulb.