Lecture number 1. The reason why I'm not using in the beginning the Powerpoint is because this lecture aims to give an opportunity to the students to understand the fundamental concept of acoustics. This lecture is not just a transforming a lot of knowledge of acoustics to the students. And this lecture is to convey properly, effectively, the fundamental concept of acoustics to the students. So that's why I'm using blackboard. At the end of this lecture, I will use the PowerPoint to summarize what I convey during this lecture. Waves, what is a wave? Waves is what transforming information from one place to another. Okay. So there is a some information like. >> [SOUND] >> And then this information will be transmitted by this median to some other place. So essentially wave handles, space or position and a time. And in a way the position, or space and time is not independent variable anymore. And the space and time is related. And we will study how this space, and time is related in this lecture. Okay, let's start with a very simple case, okay. The very simple case of the wave, okay. Mathematically very simple case is, I think everybody know this graph, Okay this is y equal x and that is y. And this is x. x is coordinate to express the distribution of information in x. And y. Is what is measured with respect to x. For example, y is the, some, some information. Okay, if it is moving in this direction. This amount, then we can write this is y = x- b, and this is -b. Okay, if b is c0t, in other words, I'm moving this y or x straight line with a speed of c0t. Then I can write so y = x- c0t. Now, the line is moving in this direction. Okay? What if I have certain shape which I may call it g of x? And if this shape is moving in space in the x direction by the speed of c, By the time, then I can write hat this as g (x-ct). Okay, this is right going well. All right, g can be straight line, g can be any sign, or sort of goal you want. Or g can be this kind of triangular shape. So generally I can say, any general way, one dimensional way, can be written. g(x-ct)+h(x+ct) and as you can see over here in this argument, this is left going away compared to. This x-ct right? If you come here again, if this moves that way then this equation is y=x+p. Right? So this is left going way. And this is right-going wave. Every one dimensional wave can be either right-going wave or left-going wave, or the sum of left-going wave and right-going wave. So I can argue that this is a general expression of all one dimensional way. Okay. General dimensional way. Is it true? It is true because nobody can argue me that there is another type of one-dimensional array. Okay. Now let's see one special case, okay, and now I have wage yxt that's propagating in x direction x- ct. It is interesting that I am observing wave g with respect to x. What if I observe wave with respect to time? That means I want to observe g with respect to time. If I use arguments of t. As in the variable over there, the physical means I'm sound with, observing with the respect time. And this means I'm observing wave with the respect x, as we can see over here. Right? This is coordinate of x. We are seeing the web propagating in x direction, but I want to see the wave with respect to time. How could I see? Okay, I locate my eyes over there. and there are a lot of wave passing through my eyes as time goes on. That is t minus, minus. X over c. Is it correct? If I divide the space with the respect of, by the obtain is the The time lapse I experienced. So, this is another way to express the right going wave, okay? Okay, what if I have sinusoidal wave? And then I can write, yxt. So, x, the sinusoidal wave k's, if it is a sine wave, then it looks like sine. And X- CT, instead of G, I pick up one special propagating wave that look like sin. So in this case, sin wave propagating with the speed of c. Okay, Is there anyone who saw sin (x-ct)? No, it's not possible because the argument of sin has to be radial, right, and x Is on a scale of x is meter in mks unit. So I need some factor that can change this x dimension to radial dimension. So let's call that as k. Okay. Introduce arbitrary amplitude. Then I can argue that this is the sine wave propagating in x direction. Okay? Now, This simple mathematical expression will provide us many interesting wave propagation property. And you were surprised. Okay, now this can be written as A sine Kx minus kct. Okay. Let me focus on this factor. What is kc? Kc has to be omega. Right, everybody familiar with the oscillating in time, is Omega. So, K, C, is related with Omega, and we know that Omega is. 2pif. F is frequency in hertz. Right. So kC is related with 2pif. Okay. Kc is related with 2 pi f and f is frequency, therefore, we can say that is 1/T and the T is period, right? And that means K is equal to 2 pi one t multiply c. What is the t times the c? So T is a period and the C is the speed of preponderation. That means that T multiplied by C is how much wave is appropriating with one period, how much wave is appropriating with one period? And that is wavelength. So we obtain that k is 2 pi over lambda. That is very interesting. K is two pi over lambda. Of course, that is From the relation over there, that is 2 pi. Okay. Omega over c that is 2 pi f over c. So, from this relation we can find that Lambda is equal to C over f. And the frequency is the measure of auxillation or wave in time. And the lambda is a measure of oscillation in space. And wavelength and frequency is not, in other words, oscillation is in time is not independent with oscillation in space, and that is vital key concept to understand wave propagation. And this is called dispersion relation. Okay, dispersion relation, simply dictate how the oscillation in time is related with the oscillation in space. Next lecture I will bring some demonstration to understand this behavior. So the frequency of 1 kilohertz, I will make a frequency of one kilohertz by my mouth, which is [SOUND]. This is 1 kilohertz. I have an app that can measure the frequency. Now, I'll show whether or not is correct. Okay, Our whistle. [SOUND] You can see the 1 kilohertz over here, and you can see 2 kilohertz. [SOUND] [LAUGH] It's not correct. [SOUND] This is 2 kilohertz. Okay, 1 kilohertz, so what about the wavelength of 1 kilohertz? So c is speed of propagation, usually, I mean in normal condition C is is 343 meters per second. So 343 divided by 1000 is about .34 meters, so the wavelengths of 1 kilohertz sound is about 40- 34 centimeter, which is pretty large. Okay, wave lengths of. When there's [SOUND]. Okay, let me see. [SOUND] Our wavelengths of this form is. I have to divide 343 by 500, so this is about 60. If you go to the bigger c that is 252 the wave lengths of bigger c is how much? It's longer than, obviously, 1 meter, 1.5 meters, things like that. So it's very large what we are handling, okay? So back to the 1 kilohertz case, the wavelength is 34 [INAUDIBLE] Transmitter. What I'm emphasizing by demonstrating my whistle in relation with this famous dispersion relation is that I'm just saying that the frequency oscillation in time is not independent frequency oscillation in time, is related with the spacial oscillation in space that is wavelengths.
