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Hey, guys, In this video, we're gonna talk about something called intensity level and how it relates to volume. Okay, let's get to it. Volume of the sound is not actually a measure of the intensity of the sound wave, but it's actually a measure of a related quality called the intensity level. Okay, so when I gave the introduction, I said, We're talking about intensity level and how it relates to volume. Well, intensity level is volume. That's how are they related to one another? Really? What we want to talk about is how intensity level and thus volume are related to intensity. Okay, Now, the reason why we use something else than intensity for volume is because volume doesn't really change that much. With small changes in intensity, there are Onley noticeably large changes in volume with incredibly large changes in intensity. Okay. And thus we use a log arrhythmic scale for intensity which we call intensity level. The intensity level, which is given by the Greek letter Beta is 10 d b times The log a rhythm of I over. I'm not where DP is our unit the decibel okay, and I not is called the threshold of hearing and it's one times to the negative 12 watts per meter square. That's the quiet it sound the human ear can hear. Okay, now, because this is a log, a rhythm it on Lee changes with factors of 10. Okay, so when I becomes a factor of 10 larger lage, rhythm becomes one larger or 10 larger because I'm sorry or the intensity level becomes 10 larger because it has a factor of 10 out in front. Okay, so it's those powers of 10. Increases in, um intensity lead to noticeable changes in volume. But if we go from, let's say ah, 100 to 102 watts per meter squared that produces no noticeable change in volume. If we go from 100 to 1000 that produces a noticeable change in volume. Okay, so we use a logarithmic scale because Onley those multiples of 10 and intensity really produce noticeable changes in volume. Alright, I threw on some common volumes for you guys here. The threshold of hearing is by definition, zero decibels. This is because beta right, which is 10 DPS log of I over I Not if we say I'm not over I not. This is one and by definition, the log rhythm of 10 So the threshold of hearing the quietest sound that you can possibly here is zero decibels. A quiet room, about 40 decibels. Conversation about 60 decibels. Probably what I'm speaking at a at about now inside of this room, speakers in a noisy club. I'm from Miami. So we got lost noisy clubs down here. 100 decibels or so threshold of pain. When it starts to hurt your ears is 130 decibels. Just to give you a little bit of context. A jet aircraft, like a 7 47 150 ft away is already above 130 decibels at 140 decibels. Okay, dangerous volumes or above 150 decibels. That's when you start to cause serious damage to your ears in the short term, not the long term, Okay? And theoretically, there are volumes that can kill you, which are usually a theorized to be about above 200 decibels. Okay, but it's obviously never been proven. All right, now the thing is, just because they sound is loud enough it has a volume above zero decibels doesn't mean that a human can hear it. Humans can't hear every sound above zero decibels because sorry, I minimize yourself too quickly because there is a range of frequencies that humans can hear at. Human. Hearing is considered to be between 20 hertz and 20, hertz or 20 kilohertz. Okay, but we can still feel the effects of very, very loud sounds. Even out of the range of hearing for us, for instance, sounds that dangerous volumes at 150 decibels arm or even if they're outside the range of hearing we can feel the pressure coming from the sounds. Okay, that pressure is still of physical. That's still a physical thing, and that pressure is putting a force on our body, even if we can't hear it. All right, let's do an example to close this out. Sound is measured to be 25 decibels loud at a distance of 10 m from the source. If you walked 4 m away from the source of that sound, what would be the volume of the sound? Okay, so beta one is 25 decibels, and this occurs at a distance are one of 10 m. Now Beta two is our unknown and this occurs at a distance of our two. 4 m further away than our one or m. Okay, now the process to solving this problem is a little complicated because, or at least complicated algebraic Lee, because it involves logarithms. But this is pretty much the way you're always going to solve these problems. They're all usually presented in the same way, except instead of maybe walking away, they have you walk towards the sound, but it's pretty much the same problem. The first thing you're going to start with is the relationship between the intensities. The idea is that beta, too, is 10 decibels. Log of I two over I zero. You don't know what I two is and you can't find I too, because you don't know what I one is. But you can express I to, in terms of I won. Once you've expressed I to in terms of I one. Then through some algebraic trickery, we can get 10 decibels log of I won over I not, which is by definition, beta one which we know so we can solve the answer that way. Toe find the relationship between I one and I two. We just need to use our regular old intensity relationship, right? It's the reciprocal. So it's our one over R two, so I to is gonna equal are one which is 10 over 14 squared I one which is about I want Here's where that algebraic trickery comes into play baby too which is decibels log of I two over. I'm not. I'm gonna replace to with the substitution I just found for I won. This is 10 decibels log a rhythm of 051 I won over I not now for a log, a rhythm Any time you have the multiplication of two numbers. In this case, when a multiplying is 20.51 and I won over, I not those are my two multiplication. Any time you have the multiplication oven input for log rhythm, you can split that into two logarithms that air summing together. Okay, so this is equivalent to 10 decibels. Log a rhythm of that first multiplication plus 10 decibels log rhythm of that second multiplication term. Okay, And remember, this right here is just beta one by definition, and we know what beta one is. It's 25 decibels. This right here we can plug into a calculator and we find its negative to nine decibels. All right, I'm gonna get myself just a little bit of room here to finish out this problem. So be the two is 25 decibels minus 29 decibels, which is 22. decibels. All right, And that's pretty much how you're gonna solve any of these problems. They all are pretty much the same. And it comes directly from this log arrhythmic trick that the log of a times B equals the log of a plus the log of B. That's that little log arrhythmic identity that we want to use. If you guys don't remember your log rhythm identities, you're logarithms algebra just for this part. Specifically in this chapter, you should review it just a little, because it will come in handy. Alright, guys, that wraps up our discussion on sound intensity and volume. Thanks for watching

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