When raindrops fall onto a pond, you can see that the waves propagate away roughly in circles. You can also see that water waves can pass through each other. When they do, their heights simply add together. This is called superposition or interference of waves. Light waves also add in this way.

The waves on the left have the same wavelength and amplitude. They are also in phase. That means that their crests and troughs happen at the same place. When these two waves add together, the resulting amplitude is twice as high. They are said to constructively interfere.

The waves on the left have the same wavelength and amplitude. They are also completely out of phase. That means that their crests and troughs happen at opposite places. When these two waves add together, the resulting amplitude zero. They are said to interfere completely destructively.

The top two waves have different wavelengths. They are in phase sometimes and out of phase sometimes. Their superposition is more complicated. The pulses seen here are called beats.

Please go to the website of Dr. Dan Russell and view the animations involving superposition of waves found here:

Superposition of waves - Dan Russell, Grad. Prog. Acoustics, Penn State

The to two above waves were added mathematically to produce the superposition of waves shown on the bottom axis. The ratios of the wavelengths used in the program was the correct ratio for adding red and green light to result in yellow light. Red has 1.25 cycles, green is about 1.75 cycles, yellow is about 1.5 cycles

# The wave nature of light

In the early 1900's, there was a big debate among physicists about the nature of light. Some thought it behaved as a wave, others believed it behaved as a particle. To gain an understanding of how light behaves as a wave, let's consider two identical waves that add in superposition.

The sound waves in this PHet simulation show an interference pattern as they add. Notice that where the troughs (dark regions) coincide, the color gets darker. Similarly the intersection of crests is lighter. Also, where the waves destructively interfere, the shade of gray is the same as the equilibrium background color. Notice that there are v-shaped lines emanating between the sound sources that stay at equilibrium. Think about what it would look like if you could see a slice of the added wave where it passes a certain distance from the sources. You would see a pattern of light and dark that would indicate that waves had been added.

Please visit the PHet site at phet.colorado.edu/en/simulation/legacy/sound and run this simulation. See how the signal changes as you vary the amplitude and frequency of the waves.

This simulation shows sound waves, which are compression waves. Light waves behave similarly as they pass through a slit. In your lab exercise this week, you will investigate the behavior of water waves, sound waves and light waves as they are added together and look for evidence of the wave nature of light.