Wave Reflection

by Patrick Ford
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Hey, guys, in this video, we're gonna talk about reflection of waves. Let's get to it. When a wave encounters a boundary between two media, it could do two things. It can reflect off of that boundary or it can transmit through that boundary. Okay, Waves will actually do some of both what we would call reflective surfaces or surfaces that Onley allow reflection like light off of a mirror. And what we would call transparent surfaces are surfaces that mainly allowed transmission like a window that mainly allows, um, are very, very, very thin window mainly allows, like coming through on most windows. Though you have a bit of reflection of light, you could see a reflection in the in the window and transmission of light, like from outside, is coming through that window so you can see the outside world. Whenever a wave encounters boundary, it exits the boundary at the same frequency. Okay, this is another fundamental fact of waves. Okay, you have to remember this that no matter what situation when a wave encounters a boundary, it exits that boundary with the same frequency. This is true, regardless of whether it undergoes transmission or reflection. So if it transmits, it enters the new medium with the same frequency. If it reflects, it stays in the same medium with the same frequency. Okay. And this is another fundamental feature of waves. All right, now imagine a wave heading to a wall. Let me minimize myself so we can see this figure this boundary will say does not allow transmission of the wave. Right? It's a wave on a string, That wave, meaning that string has no way of passing through the wall. So the wall, which is that separation of media, prevents transmission when the wave encounter the wall, though it is going to reflect off of it. So it's going to come in, it's gonna get close, and then it's gonna reflect away. The reflected wave will have the exact same frequency as the incident wave right, the wave approaching the boundary. But it is inverted, right? We see here that I drew the wave upside down because when the anchor point is fixed for a wave, the reflected wave is going to be inverted, and the reflected wave then just travels back towards the point of its origin. So if you're over here whipping the rope up and down, producing these waves thes waves. They're gonna propagate forward, reflect off of the wall and then propagate back towards their point of origin. Okay, Now imagine a different scenario. We have a wave on the light string heading towards a portion of the string. That is heavier. Okay, We're gonna say the mass per unit length of the string increases. This is a boundary right here between two media, because the wave in the first string is in a medium where the mass per unit length is low. And then any waves on the second portion of string is now in the new medium, where the mass per unit length is much higher. Okay, this boundary allows both transmission and reflection. Okay. The transmitted pulse is gonna have the same frequency and is going to be upright. The reflective pulse is also gonna have the same frequency, remember? Same frequency, regardless of whether it's transmission or reflection. But the reflective pulse is gonna be inverted. Okay, Just a ziff. It was bouncing off of the wall. Alright. If there are multiple ways of stretching, if there are multiple waves stretching along the entirety of the string instead of just a single pulse. Meaning as you have pulses bouncing off the boundary, they're gonna come back and interact pulses going towards the boundary. You're gonna have a whole bunch of interference along that stream. We already talked about how waves when they occupied the same position at the same time, are going to interfere in the specific instance of a wall. What you're gonna have is you're gonna have a string, right, with a whole bunch of waves coming towards the wall and a whole bunch of inverted waves coming off of the wall and those inverted waves and those upright waves are gonna interfere once they cross over each other. Okay? And this is actually a specific scenario that we're gonna talk about in a little while. Okay, let's do an example. This isn't a quantitative example. This is just a qualitative example. Whenever a string is fixed at a boundary, the wave along the string reflect off the boundaries always inverted. Why is this so? Would the way it be inverted it? The string were free to move at the boundary. So let's consider. Let's consider two scenarios. One where our rope is fixed at a wall and one where a rope has a little ring here that's free to move up and down without any friction. And the wave is moving well, the reason why waves when they encounter a boundary that they're fixed that are inverted coming off is because when the wave reaches there, it pulls up on the anchor point. This is putting a force on the wall and the wall puts an equal and opposite force back onto the string, and that pulls it down and inverts it. Without that fixture point, you are gonna have that equal and opposite force. What's gonna happen here is when the wave reaches here and it lifts up, there's not gonna be a force pulling it down. This loop is just going to go up, okay, so it's gonna go up and then it's gonna fall back down, and it's exactly as if you whip the string from the other side. Okay, so this is gonna have inverted waves reflected off of it, and this is gonna have upright waves reflected off of it. If you were tohave the end free to move at the boundary. Alright, guys, that wraps up reflection of waves. Thanks for watching