Let's look at this graph, this famous graph. Okay this is 0dB and this is 60dB that corresponds to normal the sound pressure level in working area okay. If you have a very loud sound like a jet noise, that will be between 100dB or 130dB, 140dB if you want to get them in linear scale, the p scale average should be 10 to the 14th, right? That is very big sound. I don't know whether you guys really have a chance to listen reject noise but I'm sure you have chance to hear the very loud rock and roll music for example, okay. That corresponds to about between 110 and 120db. Okay lowering down over here. When you discuss together okay, very anticipated discussion. Everybody wants to talk and with a passion and energy. Okay that corresponds to about 70dB. If you go to the library hired and the library I mean which is used to buy so called the civilized students. Some pressure level about that is between 30, 40db. For example, if you go to a very expensive the restaurant which requires you dress codes very calm which will be about 30 DVA. So, now you have the feeling about decibel scale. So, you now have idea, very rough idea about the decibel skill, right? So, let's move to another one. Okay, this demonstrate how you feel about different decibel scale 6db, 3db and 1db. Okay, 3db is corresponding to a very interesting all case, Sound Pressure Level or Lp that is define the F ten low. 10, 10 stands for deci and this value we call bell. So we call this is decibel and we see P means scale pressure. Reduce that to the scale of reference pressure, and reference pressure is 20 micropascal. What's 3db means? Okay, if P squared average is 2 times of P squared reference then I calculate 10 log 10 3 plus 0, right? And 10 log 10 3 is what? What is 10 log 10 3 is what? Seven? What is log 10 to the 2? [INAUDIBLE] >> 0.3 something. So 10 log of 10 2 is 3. So if p scale average is two times p scale reference then we got 3 db. Suppose we have, P scale average of a certain signal. Is twice our P scale average of some signal, then what we will get is 10 log of 10 2, plus 10 log of 10 P squared average, 0 with respect to P squared reference, right? So the increase of decibel scale is 3 db in other words when we have been square pressure that is a twice all the pressure something then we will get 3 db increase. So 3 db has very important meaning. For example, if it has, if you have this signal say this is 60 dB and then you have exactly the same signal, same time then you will get three dB increase, not two dB increase What's 3 db increase. If you have [SOUND] this is 65 db, and if you a [SOUND] two 60 db then what db you will hear? 63 db. So 3 db difference. Has a very significant meaning and another one comes from actually Psychoacoustics. The minimum level of some pressure level that human being can, can recognize as the difference is through DVA which is very close to 3 dB. [NOISE] Which is about 60 dB, one kilohertz. When I increase this by 2 dB. [SOUND] I increased, believe it or not, because it's not possible to measure. Supposed I increased about 2 dB? You may think that it is increased. You don't know whether it's increased by 2 dB or 3 dB, but you may think that something has increased subjectively man that is 2 dB. So it has a significant meaning whether you can hear, you experience about 3 dB difference and the 60 dB difference and 1 dB difference. So let's demonstrate this. This is white noise. [NOISE] That is 6 dB difference. And what about There's a 3 dB difference, and what about 1 dB difference? Comparing with the 3 dB difference or 6 dB difference, what do you hear? The SPL difference by 1 dB is very, very, very small. You can hear the difference because it is sort of transient signal. You can compare directly with what you hear just before. Well for steady state sound, it's not as I mentioned to you, 2 dB difference is minimal SPL difference that you can feel that there's some difference. So that is very interesting, that means even if you reduced or increase the twice of your sound when you are hired by somebody else. And you maybe very proud of achieving that you reduce the noise, but in magnitude of twice. But in dB scale, your supervisor just can hear that there's some decrease, just a little decrease subjectively. In linear scale, you claim that hey, this is a big achievement because I reduced the noise by half or increases the sound twice. But evaluation is performed by hearing and the hearing system on it barely recognized the increase or reduced the sound. So as I said again, the objective measure and subjective measure is quite different. Now, lets move to the another case frequency scale. Frequency scale we also use logarithmic scale, because what we hear lowest to frequency literature said we can here not me? What very healthy young people can hear is 20 hertz. And highest of frequency like you guys, young, healthy, I'm sure you are all healthy. Young healthy people can hear is about 20 kilohertz. And do you have a feeling about 20 hertz? And do you have a feeling about 20 kilohertz? Of course you do have a feeling about 1 kilohertz, which is [NOISE] this is 2 kilohertz, but You don't have a chance to experience above 20 kilohertz or 20 hertz or maybe 30 hertz. So let's see what it means by frequency. What it means by frequency, as you can see here in this demonstration. The frequency is? What is the frequency mean? 1 hertz means something is back and forth in 1 second. That is 1 hertz, this is 1 hertz, because this is 1 second. This is 1 hertz, over there at the top it says 0.5 hertz, meaning something is oscillating with a period of 2, that is. [SOUND] And if it is 2 hertz that means the period of oscillation is 0.5 seconds so that is. [SOUND] So if the frequency is getting higher and higher that means the period is getting shorter and shorter. So [SOUND] means that the oscillation with respect to frequency is 1 kilohertz, and the period is 10 to the minus 3 seconds. We cannot measure it every time, but if your ear is trained by recognizing the frequency, that will be nice. Back to the SPL level. We do have a certain idea or what it is 60 dB, what it is a 130 dB and what's 30 dB. 30 dB corresponding to very quiet restaurant or very quiet library. By the same talk on we would like to have a certain feeling about of frequency too. Of course, to you already have some reference about 1 kilohertz, because I demonstrate a very often. [SOUND] Now let's see other scale. And now, as I mentioned earlier, all double range in with respect to frequency ranges from 20 hertz or 20 kilohertz. And the music ranges as you can see in this demonstration, start from few hundred hertz to. Less than 20 kilohertz, okay? And the speech normally use smaller bandwidth over here. Okay, now let's examine how you hear, how your ear system can hear. So let me ask you to draw in your notes, The following graph. This axis you draw 125 hertz and 250 hertz and 500. And then 1 kilohertz, and then 2K and 4K, And 8K. And then you put the tick mark over there. Starting with over here 10, 9, 8, 7, 6, maybe 1. So your tick marks starting here 1 to 10. Okay, everybody finish? Now, I will, Make a sound of 125 hertz in the beginning, and you will hear the sound of frequency 125 Hz, which will come like [SOUND], okay? Intentionally decreasing the sound SPL, designed SPL. Then you counted how many 120 hertz you hear, okay? To have a relatively meaningful measurement, we will give you a chance to hear 125 hertz sound twice, okay? Maybe you average it and then you mark it. And then let me start 125. [SOUND] [SOUND] [SOUND] [SOUND] [SOUND] [SOUND] [SOUND] Okay, let me have some of the sheets for this guys. I don't know whether you are healthy, right? Young, okay. So what he has is like the beginning 6, 8, 508 8,1K [SOUND] 10, 10, 4k, 8k 7. So comparing his plot with this plot. They're somewhat similar, right? Let me have yours, ladies. Elsie, right? You're Elsie. >> [INAUDIBLE] >> Hope so [LAUGH]. Okay, her case is 5, 6, 7, 8, 2K 9, 10, 10. Women hear higher frequency than. How about yours? Nothing? So you didn't hear anything. Okay, so what about you? >> I'm too confused. >> Confused? So your one is, what about? Okay, his one is the beginning, 6. 8. 8. 8. 2K 9. 8, yeah, good. Similar with the graph we show. So actually, even if we have a very bad experimental condition because of noise as well as what you hear has to be involved in room acoustics. So what we confirmed by this rather crude experiment This curve does have some meaning, right? What does it mean? In the frequency range at like one, two in this range, we hear very sensitive, okay? This range and that range is not as much as sensitive what we hear in this range, okay. So, human that they hear our hearing system, depending on the frequency. Some frequency we here very sensitively and some frequency we do not hear very sensitive as the frequency in the range of one kilo, two kilo, four kilohertz. Why? Maybe to [INAUDIBLE] some of the alarm system, or maybe to effectively communicate. It has to be tested subjectively, but, this is in fact what our hearing system does hear the sound, okay. So, we see the sound hearing system in pressure level SPL, with respect to SPL scale. And also we examine our hearing system with respect to octave scale or frequency scale, okay? And another interesting, so, it ends up having sort of equal loudness contour. What does it mean by equal loudness? In other words, that every curve provides equal loudness. In other words, loudness is a measure of how we feel about a sound. How you feel? In other words, how we loudly hear the sound. For example, over here at one kilohertz, this is 20 decibel that is 20, okay. And 120, or 250 hertz, this is actually a little bit less than 225 dB, but we hear the loudness as the same as what we hear at 1 kilohertz, okay. So, for example, if you hear 20 decibel over here, along this line means that, over here it is 20 decibel. But in this frequency, we hear the loudness about ten, different. So, this curve shows the equal loudness, okay. Based on what we experience to before.