Okay, let's start lecture Number 11. We will start to talk about the radiation, at the same time scattering. And the diffraction, and rather unified way. The reason why I'm saying this is unified way, will be addressed later on. Okay radiation, a simple radiation problem. Is as you saw before, one dimensional case, when we have a wall, if it oscillate with the frequency of omega, obviously this oxalation will force the fluid to oxalate therefore, there will be some wave propagating into force reaction, this is a very simple radiation [COUGH]. What are the important characteristics of this radiation is that, the wave observed, at any points with respect to this coordinate X, can be expressed like P not exponentiation minus J omega T minus KX or plus KX. And notes that's at any points the magnitude of pressure is constant, at any point the magnitude of pressure is constant, okay, if we invite the concept of wave front. Okay, wave front, which means that, the surface or plane where, the phase of wave is constant, okay, for example if you look at the wave at this point say X zero the wave front, it's caused on this does not depend on this direction, okay. So essentially this kind of a wave does not have near field or far field a concept, because we front this constant, and because the magnitude of Acosta's query is always constant. So everywhere, where front is constant, so, no far field or near field because of that, in terms of measurement point of view, you can put, we can put microphone anywhere. Then you can measure, so that is a very simple case. We do also understand that this case, I mean, this concept can be used for the case, when we have war, and when we have instant wave, and reflected wave and transmitted wave, because this is equivalent with. Having blocked pressure, which is 2PI, plus radiation of the war into both side. Therefore, at chapter three, chapter three, I said the understanding radiation provides us to understand the, for example, partition problem. So, let us expand what we understood about this to rather general case, okay? Suppose, I have this kind of very irregular seed vendor type of radiator, which would vibrate, Like this, With a certain amplitude. This amplitude could be varied with respect to space. That mean we'd like to know how this kind of radiate in space. Obviously, the pressure field induced by this kind of radiation at arbitrary position in time, will no longer be, the form like this. In other words, in a far field it looks like, you know, later on when we find out in the far field it look like a plane wave, the near field it exhibits more complicated form. So as we did always, to understand that this kind of problem, this chapter would talk about a very simple radiation phase. So let's start to see, this problem by seeing one simple case, which is breathing sphere case, it is an interesting name because, and then breathe uniformly breathing sphere, therefore all the fluid of particles surrounding this fuel move With the same face, okay? We may use now the velocity potential to describe this. And that can be, has to form some amplitude divided by exponential -j (omega t- kr), in one dimension, because the wave front at any position away from the center with a distance of r would be the same. Which we recall, I mean, symmetric with the respective point, okay? And it should have this kind of form. The reason why it invite this velocity potential, rather than using pressure here is because velocity potential is very useful. Because the gradient of velocity potential will give us, for example, if I take a gradient of this velocity potential with respect to space in this case. Only dependency on space is with respect to r, this will give us the velocity in r direction. Okay? And also, if I take a derivative of this velocity with respect to time, this will give me the pressure. [COUGH] All right? It'll give us the directly the pressure. So velocity potential is very useful in analytic or computational sense. Because if you got this, taking a derivative with respect to certain r direction that will provide us the velocity in that direction. And if we take the derivative with respect to time, this potential function provide us pressure. So, it's computationally very convenient, of course. That's why in old days, many people in acoustics use velocity potential when they try to compute something which has interest. Okay. So we will start to see what's going to happen when we have this kind of simple, or simplest radiator. Another simplest radiator would be the sphere, but it is oscillating. In this direction, therefore in this case sound is radiating in both direction very effectively, but no sound radiation in this direction is certainly gives us an idea what is the meaning of directivity and so on. So we will use that as a representative radiator, okay? And later on based on what we learned from these two case, we will examine the radiation from baffled piston. In this case we have a baffle and the piston is oscillating with some frequency. We would like to know how this radiator produce the sound in space. Say if this is a over 2a and then the wave is propagating like that. The sound wave over this direction would have a smaller radiation efficiency, but you have a very strong radiation efficiency along this axis. Again studying those kind of radiator we could have more understanding about the radiation through activity. Having understanding this, this chapter explains the idea to this case. Because we do understand the radiation of this case. Suppose we have a wall. We have an opening. If there is instant wave coming in. Then this part would be excited, and through the particle of that part excited, therefore it will have some velocity, then it will radiate. We will show how this understanding of this will be related to that, okay? And then I move the problem to say there is a very long wall, and no wall over there. And we will see how the wave will be diffracted by the presence of this kind of wall. Obviously, there will be very small radiation over here, and then some radiation to that direction. So, I want to expand that understanding, this understanding, to this case. So, half space case. And then I will invite what will be changing if I have a wall. If I have bottom over there. So, By approaching, What's going to happen in scatter diffraction and radiation? Using this simple case and that case, we can go to this rather complicated case. Therefore I said this is sort of unified approach. What about the scattering? Okay, I have some scatter that if there is instant wave, then as I said. Over here. The scattering problem or oscillator is equal to the pressure due to the presence of this scatter, that is similar with block frequency over there. Plus, plus the radiation. Due to this scatter. So if you understand the radiation, then you can understand the scattering, too. Therefore, I can bravely say if you understand the radiation of this breeding sphere and the trembling sphere and next go to the radiation due to baffled piston, then you can establish the foundation of our understanding to understand every radiation or physical phenomenon of scattering diffraction problem. So this is very important and essential foundation to understanding every thing related with the scattering and diffraction. Okay, let me demonstrate before I go into some of the details. Let me demonstrate some of the sound source. Okay, this is very well known Korean Jing. Which is not the same as the Chinese gong, okay? [SOUND] Okay, what you hear in the beginning, it's quite different what you hear now. Let me demonstrate again. [SOUND] [NOISE] Okay, in the beginning you can hear lot of high frequency component. But now you can hear only very low frequency component. You may argue that high frequency component means that actually the fluid particle in very high frequency. Therefore there are a lot of chance to lose energy compared with the low frequency case. But hear again. [SOUND] And the radiated frequency content is changing in this case. This is a very typical and very unique feature of Korean gong. In the beginning because hit the gong, I hit the zing with a large force the jing is deflected by a large amount and then later on the deflection of zing is getting smaller and smaller. So in the beginning, the stiffness of jing is considerably smaller than the stiffness of jing after having some enough time. So the vibration characteristic of jing is changing with respect to time. So this is a very typical nonlinear type radiation. And another feature you can hear, you listen, you experience from jing is that, [SOUND] [SOUND]. If I rotate this jing, then you can experience, some case, larger sound, some case, small sound, okay? [SOUND] This case you will hear very large sound. This case you will hear a very small sound. It's because this instrument vibrate like that, therefore radiation in this axis would be very effective. [SOUND] But radiation in this direction is not effective as the trembling sphere says, all right? So this is interesting. [SOUND] Because it radiate to so powerfully low frequency, it has been used as a very important musical instrument in old days, as well as in these days and in our countryside. And this one is different one. And so maybe I will use this. [SOUND] Different sound. Okay? If I use this one. [SOUND] Different sound. And then you can what you can experience is, [SOUND] this one. [SOUND] It's different because [SOUND] this one excite more high frequency compare with [SOUND] this one. Because contacting time of this one is wrong, and the area is large, therefore the exciting frequency is different, in this case [SOUND] low frequency. In this case, high frequency, [NOISE]. There are this kind of temple you hear very much in all the country side. Okay another one. When I use hand over there and I hit it. [NOISE] You will hear different sound because you changed the boundary condition. It's different, right? If you hold it, you observe sound. Therefore, there is no sound is radiating. [SOUND] Different sound, because you excite a different way. So, musical instrument is very interesting radiator. Okay? Okay. Very interesting radiator. [SOUND] [SOUND] [LAUGH] Okay. [SOUND] So I had enough entertainment for the students, so I can go to some of the maybe painful but interesting theoretical study associated with breeding sphere force.