If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:8:48

Video transcript

you are straight-up partying at the rock show here but you're a little close to the speaker it's getting a little loud you need a break here your user ears are starting to hurt so you back up and my question is sounds like a stupid question but I don't think it is why does the sound seem softer when you're farther 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 going to represent that sound wave like this let's draw a circle around it here's the sound wave now 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 so 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 is going to 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 these are all the same sound wave these are just a different moments in time and so the question was to remind you if someone's over here close to the speaker why do they notice a sound that's a 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 the speaker's 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 is going to emanate outwards that means this power is going to get spread out over a larger and larger area so now that same amount of powers 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 spread over a much larger area and this is one reason why the sound is going to get weaker because if you divide by a larger area if you take that same amount of power you divide by a larger area that intensity is going to get smaller and your ear 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 you're measuring how concentrated that sound is not the total amount of sound that is on the whole surface so how much less is it going to be if I was if someone's standing twice as far away so if this person's a distance deep from the speaker and some other person is a distance 2 times D from the speaker twice as far so 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 forth of an eye and eighth of an eye to figure it out you've got to remember that these sound waves are emanating in 3d space these are 3d sound waves so these are really fears these are spheres of surface area that the sound waves emanating out along and so gotta remember what the area of a sphere is I remember the area of the sphere it's 4 PI R squared this means the power up here is going to be so power is going to equal or sorry intensity is going to equal the power divided by 4 PI R squared this means if you're twice as far away this person is twice as far away he's twice the radius away that means the area that the power has 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 4 times the area so this is actually the power over here is spread out over four times the area since the same amount of power spread out over four times the area this intensity is going to be 1/4 as much if the same power spread out over four times the area and if you were three times farther away over here what do you think the intensity would be out here the intensity since you're got three times the radius you square that three you're going to get a factor of nine this is going to be 1/9 the intensity out here so this is an important rule the intensity is going to be proportional to proportional to one over R squared lots of things in physics are proportional to one over R squared and intensity is going to be one of them of a sound wave because it's spread out over a sphere and that sphere gets bigger like R squared so 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 now an actual speaker is probably not going to be sending out perfectly spherical sound waves whoops I mean you wouldn't really want if you're going to manufacture a speaker you probably don't want the sound wave traveling back here just as much as if 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 it's going to be part of a sphere it's still going to emanate along part of the sphere this is still going to be in 3d these are gonna be 3d sound waves and so even if the area isn't spread out over exactly 4 PI R squared maybe this is only a third of a sphere or maybe it's only an eighth of a sphere or a sixteenth of a sphere doesn't actually matter what matters is you're still going to have R squared here and because you're going to have R squared that intensity oops that intensity of the sound wave is still going to be power divided by something with R squared so the power is going to be the intensity excuse me is going to be proportional to over r-squared it's going to die out like one over R squared so let's come back here whoops let's come back to this one now so that's one reason why one reason why the sound gets weaker that power is distribute 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 law some of that energy gets lost into the air here now 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 and so 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 now I'm not talking about the actual the actual coordinated oscillations back and forth of the air molecules it sound passes through 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 and 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 is a wave is traveling we call it attenuation so these are the two reasons why the two independent reasons why the sounds will sound softer one the power spread out over a larger area and to 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