Interference

Interference is any time two waves intersect and create a new wave. Many things can change when two waves interfere, either by adding together, canceling each other out, etc. In this post, we'll look specifically at what happens to amplitude.

Remember that the amplitude of a wave is the distance from the rest position to crest or trough, or just half the distance from crest to trough.

Let's look at sinusoidal waves for right now.

Clearly, the amplitudes of $6\sin x, 8\sin x$ are just the coefficients, so $6, 8$. If you add them together, they constructively interfere, becoming a total wave of $14 \sin x$, whose amplitude is $14$.

This is because $-6\sin x + 8\sin x = 2\sin x$, whose amplitude is $2$. These waves cancel each other out, or destructively interfere.

In fact there's a result that is not too hard to show: if you have two waves of amplitudes $a_1$ and $a_2$, if you superimpose them on each other, then the resulting amplitude $a_3$ will satisfy $|a_1-a_2| \le a_3 \le |a_1+a_2|$. This intuitively makes sense: they either are perfectly constructive, in which their amplitudes add, or perfectly destructive, in which their amplitudes subtract, because one wave "cancels out" much of the second wave.

One final hard exercise (this is more mathy)