# Physics & Opposing Waves

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Physics and opposing waves will require you to pay close attention to characteristics like length. Find out about physics and opposing waves with help from an applied physics professional in this free video clip.

Part of the Video Series: Such Great Physics
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## Video Transcript

Hello, my name is Walter Unglaub. And this is how is physics and opposing waves. So, here I have a cavity and two traveling waves. One wave is traveling from left to right and another wave is traveling from right to left. If we assume they have they same amplitude, we can call the amplitude A. And in this length, this cavity has a length L. So, if a resonance condition is matched, we can produce the extending inside of this cavity. The resonance condition would be given by K, the wave number. so, we're assuming that these waves have the same probability or in another words, the same frequency. Times the length is equal N-Pi, where lower case N is an integer. This would correspond to the mode number. So, how can we describe mathematically the resulting wave of these two opposing waves. When they meet each other head on, they're going to interfere with each other. If we describe the first wave, which I'll denote as Y sub one and the second wave as Y sub two. I can write mathematical functions for them. Since they're oscillating in space and time. Y-one will be given by amplitude A times sine KX minus omega T, where K is the wave number, X is the variable for space, it's position in space. Omega is the angular frequency, omega's equal to two-Pi F, where F is the frequency. And T is the time variable. Now we see that for a wave moving from left to right, there's a negative in front of omega T. We can simply switch that sign to describe mathematically a wave moving in the opposite direction. So, wave two would be described by A times sine KX plus omega T. When we add these two waves together, we can mathematically describe and predict what this shape will be. So, in this following derivation, I'm going to just use shorthand for sine and cosine. So, S is going to stand fro sine and cosine will be denoted by just the letter C. So when I add these two, I have Y-one plus Y-two, which is going to be equal to A S KX minus omega T plus A sine KX plus omega T. And I can factor out the amplitude A and split these sines into respective sines and cosines using a trigonometric identity. So, I'm going to end up with A times sine KX, cosine omega T plus cosine KX sine omega T. Splitting up the first one and then, second I have plus sine KX, cosine omega T, minus cosine KX, sine omega T. Now if I compare these four terms, I see that two of them will cancel out with each other, namely the second and fourth term. So, I'm left with a mathematical function that describes the resulting wave in space and time. Y-three which is equal to Y-one plus Y-two is going to be equal to the amplitude A times sine KX, cosine omega T, plus this term again. So, I can just write a two in the front. So, I see that if they're in phase, the amplitude will double. And that will be the shape of the resulting wave in here. And if the resonance condition matched, then the wave will just oscillate up and down. My name is Walter Unglaub, and this is how is physics and opposing waves.

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