The Resultant Amplitude of Two Superposed Waves

The Resultant Amplitude of Two Superposed Waves
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  • 0:05 Waves All Around Us
  • 0:45 Wave Superposition
  • 2:46 Constructive Interference
  • 3:08 Destructive Interference
  • 3:33 Lesson Summary
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Lesson Transcript
Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

Have you ever wondered what happens when two waves run into each other? In this lesson we're going to look at that exact scenario and how it affects wave amplitude.

Waves All Around Us

Waves aren't limited to traveling through water; they are everywhere. Every sound you hear consists of sound waves. All the light we can see consists of electromagnetic waves. You are bombarded with waves all day and all night long.

Since waves are traveling all around us all the time, they must at some point come into contact with each other. Do they smash into each other and stop, do they pass through each other without interacting, or do they do something else entirely? In this lesson, we're going to look at what happens when two waves run into each other. Specifically, we're going to focus on how this affects waves' maximum displacement, or amplitude.

Wave Superposition

When two waves come into contact with each other, they don't collide. They pass right through each other without any change in their original speed or direction. However, they do interact as they pass through each other. Only waves of the same type can directly interact with each other. This means a sound wave can interact with another sound wave, or a light wave can interact with another light wave, but a sound wave cannot interact with a light wave.

We call the interaction of waves with one another wave interference. We describe how these waves interact through the principle of superposition, which states that two interfering waves cause a displacement in the medium they're traveling though equal to the sum of the individual waves' displacements.

To try and better understand the principle of superposition, let's look at an example of what we get when two waves interfere with each other.


Red and Green Superposed Waves
wave superposition graph


The resultant wave is the purple wave created by the red and green waves interfering with each other. By using the grid, you can see that the resultant displacement at any given point of the resultant wave is equal to the addition of the displacements of the other two waves at that same point on the x-axis. Essentially, the waves are overlapping to create a bigger or smaller wave, depending on how they interact.

The maximum displacement of a wave is known as its amplitude. A periodic wave's amplitude is located at the highest point in its peaks and lowest point in its troughs. Here we have a positive amplitude and a negative amplitude. In this case, the negative sign is there to show the direction of displacement. One of the amplitudes is in the opposite direction from the other, but the magnitude of displacement is the same.


Displacement vs. Time Graph Showing Amplitude
wave amplitude graph


Since a wave's amplitude is just the maximum displacement of a wave, we can use the principle of superposition to find the amplitude for a resultant wave. The resultant amplitude of the wave we get through the combination of the two interfering waves is equal to the addition of the displacements of those two waves at the same location as the resultant wave's amplitude.


resultant amplitude equation


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