Adding waves together: interference and beats

When ordinary objects meet, they usually smash into each other, deforming, breaking, and permanently modifying each other. (Go to 0:50 in the video below)

But when two waves meet, something very different happens: each wave continues moving at the same speed, in the same direction, with the same shape and size; wave can and do pass through each other completely unchanged.

Image and video courtesy of tsca111

In any region where both waves are present at the same time, the result is simply the mathematical addition of the two wave functions: superposition.

In general, the addition of two arbitrary waves yields a result which is, well, not always easy to understand.

Today, we'll look at two special cases of superposition which produce relatively simple results. In each case, we'll first do the mathematics, and then consider some applications in the real world.

• adding two waves with the same amplitude, wavelength and frequency
• adding two waves with the same amplitude, but slightly different wavelengths and frequencies

For more information

• You can watch students create a soliton and follow its motion at
  • Shallow water wave generation from nick pizzo

• Scientists at Rice University have caused ultra-cold atoms to merge into "matter waves", and then investigated the collision of two such waves. You can watch a short video explaining their work at
  • Rice University's Bose-Einstein soliton experiment

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.