Superposition of Waves

the material or substance that propagates a disturbance or wave Your first experiment will show what happens when two waves are occupying the same region of a medium at the same time. When this happens the waves interfere with each other and the combined waves take on a new shape. You will learn how to determine that shape.

First let’s review the basic parameters of a transverse wave.

Transverse Wave Crest Wavelength Amplitude Equilibrium position Trough

Next let’s look at the superposition of some simple combinations of two waves.

constructive interference. A crest of one wave is positioned with the crest of the other wave. The same can be said for troughs. The first addition of waves that will be described involves two waves that are in phase. This is referred to as constructive interference.

This represents the displacement by the white wave alone. by the orange wave alone. Since they are both displacements on the same side of the baseline, they add together. Just repeat this step for several points along the waves.

destructive interference. A crest of one wave is positioned with a trough of the other wave. The next addition of waves that will be described involves two waves that are out of phase. This is referred to as destructive interference.

This represents the displacement by the white wave alone. This represents the displacement by the orange wave alone. Since the two displacements are on opposite sides of the baseline, the top one should be considered positive and the bottom one negative. Just add the positive and negatives together like this. Repeat this step for several points along the waves.

Finally we observe two waves that are partially in phase. A similar method of adding the waves will be demonstrated.

From the baseline measure to the “white” wave From the baseline measure to the “white” wave. Then add this to the “orange” wave. See animation. Continuing on with this process gives Note the white arrow would be zero in length here. Zero white arrows added to “orange” wave occur at these other locations. So zero added to the “orange” wave would give By overlaying the constructive interference curve from a previous slide you can tell that the curve of this slide is not fully constructive interference.

Your worksheet Read the directions – how many squares does the wave move each second? Notice how many seconds pass on each graph, especially on the back side! You need 3 colors – 2 for the original and 1 for the result.

Interference Animation

The frequency of a wave is the number of waves passing a stationary point per second. It is sometimes expressed as so many waves per second, so many cycles per second, or so many oscillations per seconds The period of a wave is the time required for one vibration. It is also the time for a wave to travel one wavelength. Period (T) and frequency (f) are inversely related.

In symbolic form or

For a wave, if the distance traveled is a wavelength (l), then the time to travel this distance is the period (T ). Since the average speed is defined as a distance divided by time then

or Remember that Therefore