We learn about the decibel scale in the last lecture. And decibel scale is defined as 10 log 10, Average being scale average meaning that I'm averaging of scale of the pressure with respect to the scale of reference pressure. The reference pressure is simply 20 Micropascal. Okay, What it means, that is the smallest acoustic pressure that very healthy young people can hear. The reason why we are using decibel scale, I explained the last lecture. One reason is we are hearing very small sound pressure up to the largest sound pressure, okay. Let's explain how we hear. And this one is very interesting. All cochlea, Has very interesting characteristics. As you can see over here, Very high frequency sound arrives on up to here. A very low frequency arrived after that. So the cochlea, Is sort of spectrum analyzer, in other words, because if you have a hair cell damaged over here, then you will not hear high frequency. If you have a hair cell damaged over there, you will not hear the low frequency. So this cochlea, distribution of cochlea, Because there is a hair cell along this, Cochlea. There is a basilar membrane and there is a cochlea. And if there is some sound, then the cochlea will respond and the hairs cell respond. The hair cells' action produces some electric voltage difference, and that is transmitted to the brain, and the brain understands, there is a 3,000 hertz of sound. Okay? And also this very interesting, our hearing system sense the frequency, not linear scale. So when I whistle one kilohertz, [SOUND] and when I hear some two kilohertz. [SOUND] Our hearing system would think that, there is, I mean two kilohertz and one kilohertz. I mean, two kilohertz or twice over one kilohertz. I cannot produce four kilohertz, [SOUND] so beyond this frequency, our hearing system thinks that is twice of the the two kilohertz, in other words, as we saw before, decibel scale, we sense the pressure with respect to this. And also, we sense the acoustic on a frequency with respect to something that recall on its octave scale. Octave scale meaning simply that there is a frequency f1, and frequency f2 is a simply twice of the base frequency. And one-third octave scale meaning that the f2 is 2 to the one-third of the base frequency. The reason why we are using this frequency scale is simply because our hearing system is, Sensing the frequency with respect to f1, base frequency. So this is octave scale, this is one-third octaves, general octave scale, 1ns octave scale can be written like that. Okay? So, if you see the frequency difference of octave scale, that's simply 70% of the base frequency. And one-third octave scale frequency then is about 23% of this, sorry, center frequency, f0. So if you have a narrow, narrow octave scale, then your bandwidth of your scale become narrow, narrow, narrow. Therefore, it is necessary to define, All this base frequency or the center frequency. Because if everybody use different center frequency, we're going to have some confusion. So, there is a sound standard. So, this is octave band center frequency, starting with 31.5. Next octave scale is simply twice of this octave scale, that's 63 and 125, 125, 500, 1 kilo, 2 kilo, 4 kilo, 8 kilo, 1.6 kilohertz. That is the standard octave scale, center frequency of octave scale. As I said before, the bandwidth of this octave scale is 70% of each center frequency. The reason why we are using this very strange octave center frequency is because, well, our hearing system. So we have to accept it. And this is one-third octave and scale. Okay? And the SPL is defined like that. Okay. This graph shows 3.15, 63, 125, 250, 500, 1 kilohertz, 2 kilohertz, 4 kilohertz, 6 kilohertz. This graph is very interesting graph, Okay? Okay, 1 kilohertz, if you go over there, this is 10. What it means by 10? 10 decibel. So I am sensing 10 decibel at 1 kilohertz over here. But at 250, To sense the 10 decibel, I need some pressure more than 10 decibel. In other words, this is 10 decibel, under 10 decibel, okay? 1 kilohertz at 1 kilohertz, when I sense 10 decibel, and either sound pressure 10 decibel. But our hearing system, Our hearing system, sensation of our hearing system depends on frequency. So let me demonstrate. [SOUND] This is one kilohertz, right, increase. [SOUND] Okay, I am increasing the 10 decibel, I mean the frequency of one kilohertz. What you hear is what you sense along this line. Okay, but our hearing system is not sensitive as we hear at one kilohertz. Low frequency use your cochlear system, your hair cell system is not sensitive as you, sensitive at one kilohertz. So to get a 10 decibel frequency at 63 hertz, you need 40 decibel, okay. 40 decibel at the 63 hertz ought, Excite your hearing system as if that you are excited at 1 kilohertz, 10 decibel, okay? So this called equal-loudness contour. In other words, how you feel the same loudness with respect of frequency, equal-loudness control. This whole graph, This whole graph is to emphasize that our hearing system, Depends on frequency, right? And it is interesting that two kilohertz and one kilohertz, we have almost the same loud and equal-loudness contour. In other words, two kilohertz and one kilohertz is both sensitive of frequency then, Why? Ask for your gut. Simply our hearing system behaves like that. At a high frequency over there, equal-loudness curve is rising. Therefore, one kilohertz and two kilohertz, we have equal-loudness, high frequency and low frequency. Our sensitivity of hearing system is changing. So, for example, at eight kilohertz, you need more then 10 decibel, to have a same loudness. In other words, simply say beyond of the one kilohertz and two kilohertz, our sensory system is not sensitive as we sense the sound at one kilohertz and two kilohertz. So for noise control issues, if you have a low frequency over there, you don't have to put the same effort as you put in the frequency range of one kilohertz, two kilohertz. That's why we need some sort of weighting. A weighting, B weighting, and the C weighting. So not only just the dB scale, we need dB A, or dB C, or db B. Mostly, using scale as a dB(A) scale. As you can see over here, this is in one kilohertz and two kilohertz, it has a general weighting. With that low frequency, we have big weighting, and high frequency big weighting. For noise control purpose, therefore, we have to use at least a dB(A) scale, not just the dB scale. Because noise control with respect to human being, we have to consider our sensory system we're weighting, so we need a dB(A). Okay? So today, we talked about many intensity. And also we talked about the octave scale as well as a dB scale at a dimension about equal-loudness control, and which provide us to use our weighting system. A weighting was,