Doppler Effect

The Doppler effect is when a source and observer move away or towards each other causing the waves to be stretched or compressed. In terms of sound, the Doppler effect can cause things to sound higher or lower pitched depending on how they move relative to you. With light, it can be shifted red or blue.

With Sound

\[f_o = \frac{v+v_o}{v+v_s}f_s\]

Where $v$ is the wave speed through the medium (always positive), $f_o$ is the frequency heard by the observer, $f_s$ is the frequency emitted at the source, $v_o$ is the velocity of the observer relative to the medium and $v_s$ is the velocity of the source relative to the medium. By convention, the positive direction is from the observer to the source.

Solving

1. Draw out the source, observer, and arrows for their velocity with respect to the medium.
2. Draw the positive direction from the observer through the source.
3. Plug and chug.

With EM Waves

\[\lambda_o = \sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}\lambda_s\]