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18. Waves & Sound

# Wave Interference

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concept

## Wave Interference 8m
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Hey, guys, In this video, we're going to talk about a phenomenon that waves undergo called interference. When two waves occupied the same position at the same time, they interact with one another through interference. Okay, let's get to it. Imagine to water waves approaching one another when they meet their waves produce what we would call a net wave will call it a net wave. For now, Imagine two scenarios first, if a peak and a peak meat. So here we have a peak and another peak coming towards each other. Okay, When they meet, there are two peaks. Add up to create one giant peak. Okay, this peak is larger or it's taller. Then either of the two peaks that went into it and then the two waves continue on their way. Okay, so they break apart and they just continue on their way. Now the other scenario is a peak and a trough. If we have a trough heading towards a peak when they meet, the peak fills in the trough. All that water pours into the trough and it neutralizes itself. The net pique is shorter. Then either of the two peaks that went into it And then they once again separate and continue on their way as an individual peak and an individual trough. Okay, this is interference. When the waves occupy the same position at the same time, they interact with one another. And we would refer to the net wave as the interfered wave when two waves occupied that same space at the same time. They interfere their displacements interact with one another. All right, I'm gonna make myself I'm going to minimize myself for this part. So we have a full view of this graph right here. Now, these air, both position versus sorry. Displacement versus position grass. So they're assumed toe happen at a single time. So if I were to draw a line right here, those two waves air occupying that exact space at that same time and those two waves are both pointing up, so they're just placements are gonna add and create one giant wave. Okay, Now, if I consider this point right here, the purple wave is zero has no displacement. The pink wave has a negative displacement. So that's going to produce this little bunk right here. Next. If I draw a straight line down through here, we can see that the pink wave is above the horizontal line, but the purple wave is below and the purple wave is further below. Then the pink wave is above, so it's gonna create a negative peak, right? A trough that it's slightly shorter than this peak was originally right. This positive is gonna take away from how large this negative is. And we're gonna get this little dip right here. And then the whole thing is going to repeat itself. Sorry, Your own color. The whole thing is going to repeat itself. You have this right here. You have that wrong color. You have this right here. And finally you have this point right here. And this is going to keep repeating itself and repeating itself and repeating itself. Okay, so this interference wave, this interfered wave is also cyclic. But it's not a simple oscillate torrey motion. So you cannot simply describe it as a single sign or a single cosine wave. Both of the ones all the to the left or described as single cosign and single sign waves. But they had different frequencies when they have different frequencies. This interference pattern looks super complicated okay, but in general, the resultant displacement that interfered displacement between to interfere in waves is always going to be whatever the first wave happens to be. The displacement of the first wave happens to be at some position at some time. Plus, whatever the displacement of the second wave has to be at that same position at that same time. Okay, not only two waves interfere. You could have an infinite number of ways that interfere. So this, technically is a. Some more waves can come into this equation as well. Okay, Now, interference occurs in two types. When the resulting displacement is greater. Either mawr positive or more negative. It's greater and magnitude than either of the waves displacement. We call that constructive. When the resulting displacement is lesser, either a lesser positive number or a lesser negative number. A lesser magnitude, then either of the waves that went into it. We call this destructive interference. All right, let's do a quick example to wrap this up. Two waves air are initially omitted in our admitted initially in phase, with a phase angle of zero right there initially in phase, because if they have different frequencies than they're no longer gonna be in phase as they continue, but they're phase angle zero if one wave has an amplitude of one centimeter and an angular frequency off seconds and the second wave is an amplitude of 1.5 centimeters and an angular frequency of 15 seconds in seconds. What is the displacement of the interfered wave at tea with five seconds and X equals zero Because X equals zero, we can ignore the wave number. Nothing about this tells us how to find the wave number. But luckily, since X equals zero, that part of the function is zero anyway, so we can just ignore it, right? Why one is just gonna be a one sign of omega one t. Normally, there would be a phase angle there, but we're told at zero and why two is gonna be a to sign of omega to t. Okay, so why one is going to be one centimeter sign 10 and for seconds, times T. And why to it's gonna be a 1.5 centimeters times sign off. 15 inverse seconds. Times T. Okay, so the interfered wave, the magnitude of the displacement or sorry, the displacement of the Interfered wave is just gonna be the some of these two at the time indicated right, this is 10. The time indicated was five seconds plus 1.5 signed. 15 time was five seconds. And so this is a negative 067 centimeter displacement. So the displacement of the interfered wave is below the horizontal axis to a displacement of 0.67 centimeters. Alright, guys, that wraps up our discussion on interference. Thanks for watching.
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Problem

In the following figure, two interfering waves are drawn at some instance in time.

a. Indicate the regions on the graph where constructive interference occurs.
b.Indicate the regions on the graph where destructive interference occurs.   