Interference

Interference is what happens when two or more waves come together. Depending on how the peaks and troughs of the waves are matched up, the waves might add together or they can partially or even completely cancel each other. We'll discuss interference as it applies to sound waves, but it applies to other waves as well.

Linear superposition

The principle of linear superposition - when two or more waves come together, the result is the sum of the individual waves.

The principle of linear superposition applies to any number of waves, but to simplify matters just consider what happens when two waves come together. For example, this could be sound reaching you simultaneously from two different sources, or two pulses traveling towards each other along a string. When the waves come together, what happens? The result is that the waves are superimposed: they add together, with the amplitude at any point being the addition of the amplitudes of the individual waves at that point.

Although the waves interfere with each other when they meet, they continue traveling as if they had never encountered each other. When the waves move away from the point where they came together, in other words, their form and motion is the same as it was before they came together.

Constructive interference

Constructive interference occurs whenever waves come together so that they are in phase with each other. This means that their oscillations at a given point are in the same direction, the resulting amplitude at that point being much larger than the amplitude of an individual wave. For two waves of equal amplitude interfering constructively, the resulting amplitude is twice as large as the amplitude of an individual wave. For 100 waves of the same amplitude interfering constructively, the resulting amplitude is 100 times larger than the amplitude of an individual wave. Constructive interference, then, can produce a significant increase in amplitude.

The following diagram shows two pulses coming together, interfering constructively, and then continuing to travel as if they'd never encountered each other.

Another way to think of constructive interference is in terms of peaks and troughs; when waves are interfering constructively, all the peaks line up with the peaks and the troughs line up with the troughs.

Destructive interference

Destructive interference occurs when waves come together in such a way that they completely cancel each other out. When two waves interfere destructively, they must have the same amplitude in opposite directions. When there are more than two waves interfering the situation is a little more complicated; the net result, though, is that they all combine in some way to produce zero amplitude. In general, whenever a number of waves come together the interference will not be completely constructive or completely destructive, but somewhere in between. It usually requires just the right conditions to get interference that is completely constructive or completely destructive.

The following diagram shows two pulses interfering destructively. Again, they move away from the point where they combine as if they never met each other.