Let me try to review what we've learned in the last lecture. We mostly discussed about intensity. Intensity reaches vector quantity. And normally we express intensity as a capital i. That is pressure multiplied by the velocity, okay. This in fact describes how much energy is transmitted through a unit for example unit surface. Say this is delta x, sorry. If I denote this is delta y and delta x, this expressed how much energy is going through this surface, multiplied by delta x then delta y. So that is in other words, net power flow through unit area. Because this is vector quantity we have to know what it means by direction of intensity. Direction of intensity. The direction of intensity is normal to this surface, or it could have some direction through the surface. That is the question. The direction of the intensity can be this direction or that direction, right? Because the power transformed to the unit surface for this case and that case is the same. Or that's new to you. All right, and also we observed that, The change of the energy per unit value has to be balanced by intense flux through the surface, okay? Or one dimensional case this is just change of energy per unit time has to be balance by dIxdx. Okay, that's quite clear. And we extensively work about notation, Of intensity in terms of complex variable, okay. So the result we have was the complex intensity which is a function of x has two components. One is average intensity and the other one is the imaginary part, which is reactive intensity, average intensity, or intensity of real part. Okay? In page 117 we can readily see this average or real part of the intensity is in fact one half of the real part of pressure times velocity conjugate. And reactive intensity is I'll get one half of the imaginary part of the pressure multiplied by the velocity intensity. In the beginning that expression is rather awkward or rather not very sensible to you guys, the reason why we are using this complex notation is because the complex notation often very convenient in handling acoustics. But as I mentioned in the last lecture, the intensity is the multiplication of pressure and velocity, therefore we had this kind of complicated expression. Okay, and also in last lecture we talked about frequency scale of sound. Which is not same as the linear scale. And we also mentioned why we use the frequency of a scale on top and one third octave, general 1 over n octave. And we also learn about the center frequency concept. Center frequency of each octave band or center frequency of each one third of octave band. One thing we've found is center frequency of octave band is normally. I mean the band width of the octave band is about 70% of the center frequency. And the bandwidth of one third octave band is about 23% of frequency of one third octave band. Reason why we are using this octave band one third octave band is simply because the frequency range human being can sense, starting from 20 hertz to 20 kilohertz normally. And then we will have some demonstration associated with this. Let's go back to the concept of the decibel scale. Okay, the scale average that I wrote that I am averaging the mean scale sound pressure like this. That's what you remember. What if I have many frequency components? For example, I had 1 kilohertz component and 2 kilohertz component and 500 component and 125 hertz component. What would be the mean square pressure? Which is well proved and described in the text. For example if I have one kilohertz and a 500 hertz sound and I scale it of course 100 hertz sound and no did I say 100? Okay 501 kilohertz. If I scale it 500 hertz sound will be scaled and 1 kilohertz sound will be scared. And also the cross term between 500 and 1 kilohertz will be produced, right. But if the period of the average in time interval is long enough, then the average of the cross term disappears. So we can prove that. Mean scale average of total sound pressure is equal to mean scale value of individual frequency component. That is very important. Let me show you why this is important by using the PowerPoint we have. Okay now this is mean square average. And we would like to know if there is a two frequency component omega m and omega n right. And what would be the scale value when we have two different frequencies. Here is the case when we have n different or m different frequency component. And our derivation shows that as I demonstrate with mean scale frequency is the mean scale frequency of individual frequency component. Therefore, I can argue that if I have a pressure fluctuation like this, and I make a Fourier transform, okay, Fourier transform will give me the frequency component at each frequency, one, two, three and m. And if I draw the mean square value of each frequency component, it looks like this. Or in terms of SPL, it looks like that. And in terms of SPL as well as one third octave it looks like this. So what you normally get is this picture. So each frequency component if this is the one half p one over pm scale. So when I add up all of these frequency components I will get total spm. Sound pressure. As I said before this component that has higher p will dominate the whole s p here because we are measuring s p in terms of and is the logarithmic scale.
