Beats and the Doppler Effect

Adding waves together is, in general, a pain in the neck; the result is complicated. But we've seen that under certain circumstances, one can find simple expressions.

If the amplitudes and frequencies are the same, use trig
If the frequencies are the same, use phasors

But what if two waves have different frequencies? As long as the frequencies are not too far apart , one can try this approach:

Adding waves with similar frequencies yields beats

If you observe a source of waves which is moving -- or if you are moving as you observe a source of waves -- then you will see a change in the properties of those waves.

The Doppler effect
- Yes, yes, the rules for the Doppler effect are slightly different for electromagnetic waves.
- You can watch the Doppler effect with this simulation
- Joe Orca takes a lunch break