Let me begin with the lecture number eight, where we continue to talk about chapter three. Waves on flat surface of discontinue. There will be many different kinds of discontinuity. Okay, simple discontinuity is I have two median, Z0 and Z1. Z0 could be air, and the z1 could be water. Or z0 could be air and z1 can be sound of certain material. Z1, z0 can be water and Z1 can be, for example, the wood or steel, whatever. Or you could have there and some [INAUDIBLE] material. And you might have some food, and you could have steel plate, and then you will have air or water. There are many kinds of discontinuity. Is possible. So to understand what happened on this kind of discontinuity or you can have. For example, just a mass type of. We call this as a limp wall, or you might have a wall that I'm not only have a mass we also have some equivalence and dash part. Or you have some general plates that allow bending motion as well as you could allow some spraying, and lamping over here and really kind of this continuity is possible. And also considering the type of incident wave. This considers the discontinuity. And if you think about the type of incident waves. Simple incident waves of course is play normal incident wave that will induce reflection and transmission. And other more general type of incident wave would be, you have incident wave that has a certain angle of incidence, theta i. I call this is pr. Then it will be reflected with a certain angle P zeta R, and also it will be transmitted with certain angle that I call transmitted angle. And again, I could ask you what if I have the discontinuity as some fractured way. What would happen in terms of reflected. And a transmitted wave. Okay, this is sort of general ] circumstances. And last question will be, what could be the appropriate measure. What would be appropriate measure, Or measures? That properly, or effectively describe this kind of physical phenomenon. So in the last lecture we introduced reflection quotient, which is simply the ratio between magnitude of instant wave with respect to the reflected wave. And also we introduce transmission, transmission questions Tao that is Pt/Pi. Okay? So to understand the meaning and importance of this two questions to which I introduced as a candidate of appropriate measures that represent all the physical behavior associated with the disc. Rather if you like complicated, physical plan phenomena We have looked at the behavior of these two measures. For the case of this very simple cases, okay? For this case, we found that the reflection coefficient is just simply, The function of the characteristic medium. That is z0 + z1, over there that is z0- z1 or z1- z0? Okay, z1- z0 then I have to use this one z1 + z0, okay? Transmission coefficient look like z1 + z0 and a 2z1, as far as I remember. And also, I remember I made the mistake to drive the transmission to lost the transmission [INAUDIBLE], and the velocity reflection velocity quotient. But I'm sure every students found where I made a mistake. Let's begin with reviewing What's the physical meaning of these things for this simple case, and then we will move on to this case, okay? So, let's see what we have. Okay, so this is what I said. So the expression we have has the form of right going wave observed with the respect to time, because it's easy to apply the boundary condition at x equals zero, over here. So, I'm applying boundary condition to get, and the relation between Pt and Pi and the Pr over Pi. So this is found the position pressure continuity, and the velocity continuity. The reason why we have a minus sign over here is because velocity of reflected wave has this direction and the velocity of instant wave has this direction and velocity of transmitted wave have this direction. And we have three equations and we have the unknown Pt, Pi, PrPt therefore we can get the ratio between Pt Over Pi, and the Pr over Pi that we call the transmission coefficient, as well as a reflection coefficient. And this is what we have, reflection coefficient and a transmission coefficient and that is pressure reflection coefficient, and a transmission strictly speaking. So that does not represent what we can hear, or what we can actually sense by the instrument. So what we hear is very much associate with the power transmission coefficient. That is pressure multiplied by velocity in real value. But if you use the complex value comp power is, as we noted before, the power of acoustic wave is pressure, complex pressure multiplied by the conjugate of, Complex velocity. Therefore, what we have Is this. This is the power reflection coefficient, and this is a power transmission coefficient. Looks complicated, so to find out what's the meaning of this power reflection coefficient, and power transmission coefficient. We have to look at this in terms of graph or experiment. But the experiment is rather costly therefore the effective way to explore what does it mean. Is look at the physical meaning in terms of graph. Se let's see the graph. Okay, this is the graph of reflection coefficient. Which is this, this is a reflection coefficient. And okay, this is transmission coefficient. As you can see here, when you get When z one is equal to z zero over here. You will have zero transformation coefficient that makes sense because two medium is identical. Okay, but when you get large and large. In Peter's mismatch, which over here is a 20. You will have big reflection corruption and the transmission approach to what? Anything wrong over there, you have a question? [INAUDIBLE] It is changed. This is tow right? And this is a? All right, thank you very much for correcting my mistake. And this is velocity, reflection as well as transmission coefficient. And let me see carefully to avoid any further mistake. And this one is velocity transmission coefficient. Correct. So if you see this tube graph at the same time you will see that the velocity of of transmission curve change is going down as the ration between the two. Medium is increased but transmission, pressure transmission is increasing so that's good, that's good because that would solve our paradox. All right, when. When I make a noise in air and I ask to you whether, or not the fish will hear the noise I'm making over here. That's the case when Z 1 is very large compared to Z 0. Okay, the transmission curves increased to two, but because the velocity curve transmission is going to. Approach to 0, so fish cannot hear my lousy sound over here. So at the fishing spot you can even turn on your radio and enjoying fishing. Okay and the power transformation quotient, and the reflection quotient turns out to look like that, and this is the power transformation quotient. And this is again the transmission coefficient of power as you can see here as the impedance ratio increases, it rapidly goes down.