Sound Intensity

by Patrick Ford
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Hey, guys, in this video, we're gonna talk about sound intensity. Intensity is a measure of sound waves. That's very that is related to the energy carried by that sound wave, but is, um or useful measurement to know? Okay, let's get to it. Now. Intensity is the amount of power carried by a wave over the surface area that that wave happens to be spread across. Okay, power is fundamental to that wave. Meaning a source admits way a wave at some power. Okay. And as long as that power isn't dissipated, it's going to remain constant as the wave travels through space. For instance, in this recording studio where I'm making this video, we have sound insulation to protect from outside noises. That means whatever sound is passing through the walls where the insulation is, that installation is supposed to absorb all the energy that sound, absorb all that power. So that sound doesn't pass through into the room that I'm filming in. Okay, now imagine a sound source. Some source of sound is admitting sound in all directions. Okay, I draw a figure here. Okay? Sometimes we call this admitting spiritually, or if you want to get fancy, we would say admitting it s a tropically. Okay, I so meaning the same tropically. I'm assuming it has something to do with direction, but I'm not sure. So I'm not gonna lie to you guys. I just know I see a tropic means the same in all directions. The surface of an area depends upon R squared, right? The surface area. Sorry. The surface area of a sphere depends on r squared. The surface area of a sphere is just four pi r squared. That means the surface area depends on r squared. And so the intensity depends on our square for that very reason that I said assuming there's nothing to absorb the sound than that powers a constant. So the only thing that changes is the sound gets further and further out is the radius of this spear that the sound is spread across. Okay, so the intensity changes the further out you go to intensities of two different distances are related by the following equation. We have I won in the numerator and I two in the denominator. Remember? The way to remember this is it's always the con. It's always the reciprocal. Okay, so our two over our one squared. If I two is in the denominator are two is in the numerator. Obviously, if you reciprocate both sides, the equation still holds. Okay, let's do a quick example. A speaker emits a sound that you measure to have an intensity of 100 watts per meter squared when you are 5 m away from it. What would the intensity be measured over the intensity measured Be if you walk 3 m towards the speaker so we have our one is 5 m an intensity one is 100 m watch per meter squared. That's just the intensity measured at our one and we have our two. We were 5 m away. We walked 3 m towards the source. So now we're 2 m away and I too is our unknown. So I'm gonna write I two over. I won and remember, it's the reciprocal. So this is our one over r two squared and that means I to is our one over r two squared times I won, which is 5/ squared times, 100 watts per meter squared, which is about 625 blots per meter squared So what does that tell us? That the intensity increased the closer you got. Okay. And this is something that we would expect because the closer you got that sphere that contained all that power amended by the source is smaller, so the power density is larger. Okay, The intensity is also related to the maximum pressure in a sound wave. Remember that. It's sound is just oscillating pressure, so it's gonna have a maximum pressure, and it's gonna have a minimum pressure. Okay, The maximum pressure is one. Sorry. The intensity equals one half times the maximum pressure pressure divided by the density of the gas that the sound is propagating in times the speed of sound. Okay, so we can do another quick example here. Air has a density of 1.22 kg per cubic meter. If a sound wave has an intensity of one time center, the seven watts per square meter. What is the maximum pressure off the wave if the air temperature is zero degrees Celsius? Okay, well, what changes? With an air temperature of zero degrees speed, what changes the air temperature of the speed of sound, but the intensity. So it's a little bit of foreshadowing there that we're gonna have to calculate. Speed is P max divided by Roe V. Now, just as a heads up, we are dealing with pressure and power here, both of which are given by capital P No, by context and by your familiarity with these equations that this p here is pressure. This is maximum pressure. This is not maximum power, right? The power doesn't change is the sound travels So rearranging this equation He Max is two i times row times v the speed of the sound. So what is the speed of sound of zero degrees its 331 m per second times one plus the temperature in Celsius which zero over 273. Right? And that is just 331 m per second. All right, so the maximum power is two times that intensity one times 10 to the seven times the density 1.22 That density is given right here already And s I units times the speed which is m per second squared and that is 81 times 10 to the nine Pascal's, which is a huge, huge, huge pressure. Almost 100,000 times atmospheric pressure that would kill you. Definitely. Alright, guys, that wraps up this introduction into sound intensity. Thanks for watching.