The Superposition Principle & Resultant Waves

Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After completing this lesson, you will be able to explain what the superposition principle is, and use it to predict what will happen when two waves are combined. A short quiz will follow.

What is the Superposition Principle?

The superposition principle is one of those ideas that sounds much more complicated than it really is. Physics can be like that sometimes. The superposition principle states that for linear systems, the net response caused by two or more inputs, is the sum of the inputs each would have caused on its own. Confused? Probably, so let's simply this a bit.

In most cases, when people talk about the superposition principle, they're talking about waves, or sinusoidal vibrations in space and time. Examples of waves include light, sound, water waves, and earthquake waves. All of these things work in the same basic way: If you take two waves and put them on top of each other -- or superimpose them -- they add together. This is what superposition is.

Let's get into some of the detail of what that means in the real world.

Resultant Waves

When two waves are on top of each other, they add together to produce a total wave: we call it a resultant wave. We call it that because it's the result you get when adding the waves up.

Waves contain peaks and troughs that come in a pattern, one after another. When you superimpose the peaks of two waves, they add together to form a bigger peak. When you superimpose the troughs of two waves, they add together to form a bigger trough. This is called constructive interference. On the other hand, when you superimpose the peak of one wave, with the trough of another, they add together and flatten out to nothing: to a flat line. This is called destructive interference. It's kind of like how -6 plus 6 equals zero. The peak and trough cancel each other out.

Superposition of Waves
Superposition of Waves

Examples of Wave Superposition

Many examples of wave superposition are hard to observe in everyday life, unless you happen to have a physics lab at your disposal. The most common example in a physics lab is the series of light and dark fringes you can get by shining light through two nearby slits.

The Double Slit Superposition (Interference) Pattern
The Double Slit Superposition (Interference) Pattern

But some can still be seen... or even heard, without any special equipment. When you sing in the shower, the reason you sound so good is because of superposition. The sound waves you produce in the air bounce off the walls and interfere with each other in a way that produces a pleasing sound. The goal of a well-designed music hall is to create plenty of constructive interference so that the sound reverberates across the whole hall. A badly designed hall acoustically will have quiet spots where the sound isn't as clear.

The Royal Albert Hall has acoustic discs suspended above to improve their sound quality
The Royal Albert Hall Has Acoustic Discs to Improve Their Sound Quality

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