6. Summary
1. This section did not involve much in the way of new material; most of it was exploring the implications of the idea of superposition:

Superposition is the way of combining the effects of two (or more) waves

To superpose two (or more) small waves, we add together the displacement of the waves at the same position \(x\) for the same time \(t\).
2. For mechanical waves this means the displacement of the medium \(\Delta y\). For sound waves "displacement" can refer to the change in pressure \(\Delta P\). For light waves it refers to the magnitude of the change in the electric or magnetic field. Mathematically, superposing the displacement of two waves can be written as
\[\Delta y_{total} (\text{at location } x \text{, time } t) = \Delta y_1 (\text{same location } x \text{, same time } t) + \Delta y_2 (\text{same location } x \text{, same time } t)\]
3. We introduced
 Constructive Interference, where the two waves added together maximally. For harmonic waves this implies that they are out of phase by \(\Delta \Phi = 0, ±2 \pi, ±4 \pi, ±6 \pi, . . .\)
 Destructive interference, where the waves cancelled each other maximally. For harmonic waves this implies that they are in phase, or out of phase by \(\Delta \Phi =± \pi, ±3 \pi, ±7 \pi, . . .\)
 Partial Interference: any interference that is not completely constructive or destructive (where \(\Delta \Phi\) is not an integer multiple of \(\pi\)).
4. Three terms contribute to the interference condition. We need to consider the combined effect of a possible path length difference \(\Delta x\), the effect of the sources being in phase or not \(\phi\) and that each wave might have a different frequency (which leads to an interference called beats).
5. The actual type of interference only depends on total phase difference \(\Delta \Phi\).
6. We also introduced the phase chart, which is a useful tool in organizing the terms mentioned above.