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# Amplitude
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**Amplitude** measures how far a wave rises and falls. A wave's **amplitude** is defined as half the distance from its highest point to its lowest point. **Amplitude** is proportional to the energy of a wave, a high energy wave having a high **amplitude** and a low energy wave having a low **amplitude**.

Let's talk about wave amplitude. Amplitude is a word used to describe the severity of the disturbance associated with a wave. The bigger the amplitude, the more severe the wave is, the disturbance is. the amplitude is the maximum displacement form equilibrium. Remember that the equilibrium is where the medium would be if it wasn't disturbed. So if there's a wave going through it, got to be disturbed, that means the amplitude can't be zero.

Alright? So let's just look at a standard periodic wave. We got amplitude here, amplitude here, amplitude here, amplitude here. You can measure it either above or below. It's usually taken as a positive number but your teacher might ask you to do something else. Most of the time it is positive though.

If you're given numbers, let's say that for example, I knew the number associated with where the medium was here, let's say it was 5 and let's say this one down here is -1. Well, then the amplitude is going to be the top 5 minus the bottom -1. So that gives us 5 minus -1 is 6 divided by 2. So that gives us 3 for the amplitude. Notice we got to divide by 2. The amplitude is not the total distance from top to bottom, it's kind of half that. Alright? Alright.

Let's go ahead and talk about some of the other properties of the amplitude. The amplitude is independent of essentially everything else that we use to characterize the wave. Wavelength, speed, frequency, period, all these things are independent of the amplitude. Long as the amplitude isn't too big, we can't ask for too much but nobody's going to ask you to deal with amplitudes that are huge. Alright, shock waves and those types of things, that's got other stuff going on. But as far as small amplitude waves are concerned, all these things are independent of the amplitude. But that doesn't mean that it doesn't have any properties, that there's nothing important about it at all, larger amplitudes mean that the wave is more severe and that means that it's going to carry more energy. In fact, it carries a lot more energy. It turns out that the energy of a wave is proportional to, that's what that symbol means, proportional to, the square of the amplitude.

So what does that mean? Well, that means if I were to double the amplitude, I'm going to get four times as much energy. Because 2 squared is 4. What if I triple the amplitude? Well, now I'm going to get 9 times as much energy. So we got to be real careful with that because it's not just you triple the amplitude, you triple the energy. You triple the amplitude, you multiply the energy by 9 because of this squared.

And that's amplitude.

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