Let's [BLANK_AUDIO] Let's think about what we learned in the in the last lecture, for acoustically large room or space, in general. Oh, we expect that the sound pressure level will decay, so like 60B down per octave of length And, and in this region we call this is direct field. Because, the and there's no reflection, therefore energy is decaying as the, the as the observation, is, is getting doubled. And we will prove that anyway, and then some oscillation due to reflection, from the wall. And then at certain distance from the source we could imagine that. Some space would provide constant sound pressure, and that this field that we call diffuse sound field. And including diffuse field up to here, we call reberveration sound field. And of course this is the distance. [SOUND] Okay. Especially for acoustically large space, Sabine's theory. Says that the aa, rate of change of reverberant sound field, with respect to time, he found it is proportional to energy density of reverberant field with respect to some characteristic time T, tau, and a minus. And later on he found that the characteristic time tau is related with 1 over open area window. And then he found that this is actually 4 over C and V over As. Then, having some derivation, we found that the reverberation period, which is defined as the time required to have energy decay 60 dB down is related with interesting number 0.161, and the volume of space and then divided by open area window. Okay that's what we learned in the last lecture. And our interest it would be. [BLANK_AUDIO] How far we can, I mean, if there is a room if there is a sound source. And depending on the position of listeners say, this is the distance R. The sound energy he will be hear, would be sum of energy he will hear. I say this is total sound energy, could be e direct plus e reverb. 'Kay. And then one could think that. There is some distance, r0 that can be regarded as a distance where we can sufficiently hear the direct sound. Okay. This kind of, you know, the interesting measure could be very valuable to evaluate the, the quality of rooms acoustics. Before we only evaluate the quality of a room assuming that the sound field inside is diffuse field. Okay, therefore, it doesn't matter where you are located. But if we think little bit more carefully that is too brave assumption, and we could think that depending on the position. The effect of direct sound field compared with the reverberant sound field will be different. So we want to find out this kind of value. That we call sometime characteristic distance from the source. In other words, there is some distance we can characterize the quality of a sound that one can hear from the room. I mean, in the room. Okay, so if r0 is very long, that means we are hearing sound mostly direct sound in the, in the large, I mean, r0. If r0 is very small, then what you hear would be, within small distance, what you hear would be mostly reverberant. So that kind of you know, distance concept would be nice. And then later on we will call this radius of reverberation. The first topic of today's lecture is to introduce radius of reverberation, okay? OKay, let me continue to talk about this [SOUND] to get the result. Okay, first in free field or direct field. We said in the graph, SPL would decay 6 dB, 6 dB per octave, or doubling the distance. Okay, let's prove this. Suppose, for simplicity, I have monopole here, and radiate sound, and say I measure power at distance r1, and then I measure sound at distance r2, and r2 is 2r1. Okay. Then I can say the power coming out from this surface would be power coming out from this surface would be intensity at r equal r1 multiply by 4 Pi r1 square that is power out and r1. That is quite straightforward. And the power out at r2 would be intensity at r2 multiplied by 4 pi r2 square. Okay, right, so and, we know that this power out through the surface that is made by the radius of r1. As to be same as the power out. Through the surface with radius of r2, because the fluid we are considering is, does not have any element that, that observes sound energy. In other words, the, the, the medium has no viscosity. So only energy decay is due to so called spreading of some. Therefore, therefore we can write according to this relation we can write I_r1 4 pi r1 is equal to I_r2 4 pi r2 square, right? Therefore, therefore again the intensity ratio, between I_r2 and I_r1 is equal to simply r1 divided by r2 square. And that is 1 over 4. Right. It's too simple? Now, then, how much sound power is decreasing in terms of log scale, and I can write like this, that is ten log ten. 1 over 4, and this is minus 6 dB. And it notes that the intensity is, intensity is. the magnitude of intensity is P multiplied by velocity. All right? And the velocity for the case of plane wave would be, what? For plane wave, the impedance is rho0 c therefore the velocity is P over rho0 c so in this case we can say that is a P square over rho0 c, right? So the intensity ratio is the same as the ratio of SPL. So we can say that SPL will reduce by 6 dB as double the, the distance from the sound source. Okay, that's good. And also recall I mean this explains the, the 6 dB down in direct field or free field when they use a direct means direct, direct field the terminology emphasise that. What we are hearing is only direct field, direct sound from the source, nothing come from the reflection. When we use the terminology free field, it emphasize that what we hear is free from reflection, so actually it has the same meaning. Okay, now this explains what's happening in free field or dialect field. But you do want to have a description that describes the reverberant field, o kay. [BLANK_AUDIO]
