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Video transcript

- [Voiceover] You are straight up partying at the rock show here. But you're a little close to the speakers, it's getting a little loud. You need a break here, your ears are starting to hurt. So you back up and my question is, it sounds like a stupid question, but I don't think it is, why does the sound seem softer, when you're further away from a speaker compared to when you're close to a speaker. And be careful, there's actually two distinct reasons for this, so let's make sure we're clear about this. It's not so dumb of a question. Here's a speaker. Now, this speaker is going to emanate sound waves out away from it. And I'm gonna represent that sound wave like this. Let's draw a circle around it, here's the sound wave. To make things simple, let's just say it sends out one burst of a sound, it's not sending out repeated sound waves, let's just say there's one burst of the sound. This is what the sound wave looks like at a given moment, the wave front. And if you wait a little while, that wave front's gonna emanate outward. So, here's the sound wave after some later amount of time. Here's the sound wave, if you wait a little longer. And if you wait a little longer, the sound wave might look like this. These are all the same sound wave, these are just at different moments in time. So, the question was, to remind you, if someone's over here, close to the speaker, why do they notice the sound that's louder from a person over here farther from the speaker. And one reason has to do with what's called intensity. The intensity is defined to be the power per area. So, this sound this speaker is sending out, a certain amount of power, and that's divided by a certain amount of area. So, right here that power is divided by this much area, that power is spread out over this much area. But the sound wave's gonna emanate outwards. And that means this power is gonna get spread out over a larger and larger area. So, now that same amount of power is spread out over a larger area. And this keeps going, the further away the sound wave gets, the larger the area. So if you're way back here, now that same amount of power is spread over a much larger area. And this is one reason why the sound's gonna get weaker, 'cause if you divide by a larger area, if you take that same amount of power, you divide by a larger area, that intensity is gonna get smaller. Notice, your ear doesn't sample the whole wave, your ear just samples the part that actually gets into your ear. If your ear could hear the whole wave, if you could sample that whole amount of power, yeah, maybe that would sound just as loud. But you only get a piece of it. So, you're just measuring how concentrated that sound is, not the total amount of sound that is on the whole surface. So, how much less is it gonna be? If someone's standing twice as far away, if this person is at a distance D from the speaker, and some other person is at a distance two times D from the speaker, twice as far. For this person up here, if this person here is an intensity I, what intensity will this person over here experience? Will they hear half I, fourth of an I, an eighth of an I? To figure it out, you've gotta remember that these sound waves are emanating in 3D space, these are 3D sound waves. So, these are really spheres, these are spheres of surface area that the sound wave's emanating out along, and so, gotta remember what the area of a sphere is. I remember the area of the sphere; it's four pi r squared. This means the intensity is gonna equal the power divided by four pi r squared. This means, if this person is twice as far away, he's twice the radius away, that means the area that the power's been spread out over is now not just twice as much area, this is r squared. Since this is r squared, if you double the radius, you're getting four times the area. This is, actually, the power over here spread out over four times the area. Since the same amount of power's spread out over four times the area, this intensity is gonna be 1/4 as much. If the same power's spread out over four times the area, and if you were three times further away, over here, what do you think the intensity would be out here? The intensity, since you've got three times the radius, you square that three, you're gonna get a factor of nine. This is gonna be 1/9, the intensity out here. This is an important rule: the intensity is gonna be proportional to one over r squared. Lots of things in physics are proportional to one over r squared, and intensity is gonna be one of them of the sound wave, 'cause it's spread out over a sphere. And that sphere gets bigger, like r squared. This is actually a little bit of a simplification, but this is one reason why the sound waves get softer the further out you go, because that sound, that power is now spread out over a larger area. It's an oversimplification, because, let me show you why. It's an oversimplification, because, if you had an actual speaker, an actual speaker is probably not gonna be sending out perfectly spherical sound waves. Oops. I mean, you wouldn't really want it. If you're gonna manufacture a speaker, you probably don't want the sound wave traveling back here just as much as it travels in front of you. You want the sound to go in front of the speaker. But it doesn't even matter. Even though it might not be a perfect sphere, if it's gonna be part of a sphere, it's still gonna emanate along part of the sphere. This is still gonna be in 3D. These are gonna be 3D sound waves. So, even if the area isn't spread out over exactly four pi r squared, maybe this is only a third of a sphere, maybe only an eighth of a sphere, a sixteenth of the sphere, it doesn't actually matter. What matters is you're still gonna have r squared here. And because you're gonna have r squared, that intensity of the sound wave is still going to be power divided by something with r squared. So, the intensity is gonna be proportional to one over r squared. It's gonna die out like one over r squared. Let's come back here, oops, let's come back to this one. That's one reason why. One reason why the sound gets weaker, that power is distributed over a larger area. There's another reason why. The other reason why is that... I lied again a little bit. This power gets diluted over a larger area, but this power, some of that energy doesn't even make it over to the second person. Some of that power gets lost, some of that energy gets lost into the air here. I don't really like that term, it doesn't really get lost, we know where it is. But energy is lost, and by "lost" we mean it gets turned into E thermal. Thermal energy of the air molecules in here. It's not really lost, it's more like it's just unavailable. It's just stuck in the random thermal vibrations of the air molecules. I'm not talking about the actual coordinated oscillations back and forth of the air molecules as sound passes through them. I'm talking about just random vibrations in random directions of the air molecules. This takes energy away. So, this is one more reason why this person farther away will hear a softer sound. Not only does that energy get spread out over a larger area, some of this energy gets lost. This has a specific name, this is called attenuation. Attenuation is referring to the fact that some energy gets lost to the medium itself. So, whenever energy gets lost to the medium, through which a wave is traveling, we call it attenuation. These are the two independent reasons why the sounds will sound softer. One, that power's spread out over a larger area. And two, some of the power doesn't even actually make it to where you're at, because it gets lost due to attenuation in the medium itself.