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Current time:0:00Total duration:13:03

Video transcript

let's say I've got a rope that's my rope and what I'm going to do is I'm going to take the left end of the rope and I'm going to jerk it up and then back down and we're going to talk about what happens or what possibly gets formed so if I take it up over here it's going to obviously take the string to the right of it up with it and the string is going to look something like this it's going to look something like that now I'm going to jerk immediately jerk it back down and as it passes let's see what the rope will look like when the left hand point is at kind of its original position yet so the left-hand point I pulled it back down but in the last time period this part of the rope was already it had some type of an upward velocity you could imagine it that way and even after that point even though this left-hand point starts getting moved it starts getting pulled down this point right here still has some upward momentum so it's still going to keep moving up maybe at a slower pace because it's starting to be tugged down by the rope on its left so it's going to look something like that and it's going to bring the rope to its right with it so the rope will look something like this the rope might look something like that and then I'm going to take this guy this this was just an intermediate intermediate position on the way to being pulled all the way down here being pulled all the way down I already used yellow let me use orange pulled down all the way down here so what's the Rope going to be going to look like now well this guy he's essentially he was he had some momentum that got him there but then all of that velocity will essentially go to zero because he's being tugged by the rope to the left and now he is going to switch directions and he will have gotten here at that point the PERT the point on the line that was here in I guess on the purple period of time it had some upward momentum so it's just going to keep going or maybe the slower pace and it'll be there and it'll bring the rest of the rope to the right of it with it so now my rope is going to look something like this it's going to look something like this and then finally where I'm going to jerk the rope back to its original position so this left-hand point is going to be there when the left-hand point is there this guy in the previous in the previous time period was moving down rapidly so he might get there ready to switch directions again and this guy will start moving down this guy right here he had some upward upward momentum so he's going to be up in this position now and he's going to be ready to switch directions so finally when I've done this whole cycle when I moved up down and back there again my rope might look exactly like this and I could let go of the rope I could just leave this left hand this little left point right there and this lump is going to propagate along the rope because in the next moment of time what's it going to look like this guy is going to be pulled up by this left-hand point so he'll go back to his resting position this guy is being pulled down but right here by the part of the rope to the left of him so he's going to be pulled down this guy is being pulled down but this guy had some upward momentum in the time period before so he will have moved up and so in the next very next time period my rope is going to look something like this it's going to look something like that and this disturbance in the rope if I do nothing else and if I don't lose energy to heat and friction and all of that it'll just continue moving down the rope if I look at the rope at some you know future period in time maybe not that far down the rope will look something like this and if I were to keep watching it I'll see this disturbance you know I keep using the word disturbance because there's really no better word to use for it I'll see this disturbance or perturbation or whatever you want to call it moving along the rope and so when we think about what a wave is we essentially I mean you know I I kind of jumped the gun I keep calling this a disturbance because I didn't want to use the word wave I want to say well what really is a wave and a wave really is just this disturbance that's propagating down the rope so this is a good time to actually define a wave a wave because once I define it I can start calling this a wave as opposed to a disturbance propagating down the rope so a wave is a disturbance the disturbance propagating through space propagating through space and you might see other definitions of a wave one of the most typical ones is is energy or a disturbance propagating energy through a medium and when they say medium it's you know what is the wave going through so in this example the rope would be our medium but the reason why I don't want to use that definition of a wave is because in future videos we'll learn about electro magnetic waves and those don't propagate through any medium they propagate through a vacuum so to keep things as general as possible we'll just call it a disturbance that propagates through space and it usually transfers energy usually transferring energy usually transferring transferring transferring energy what I mean by transferring energy well on this left-hand part of the rope I gave a little energy to the rope I moved it up down and then back again and then after I did that that up down back again is happening successively to every point to the right on the rope so you know if I wait long enough at this point on the rope right here it's going to move up down and then back again exactly what I did over here it's going to happen to this point on the rope and then later on it's going to happen to some other future point on the rope so that energy that I originally put in on the left-hand side of the rope is being transferred down the rope if I had if I had some type of a you know some type of object here sitting on the rope maybe when the when the when the wave when the disturbance passes by it this thing could get flipped into the air might get pushed into the air and go into a higher potential energy so I am so this this disturbance is transferring energy in this case now what I've drawn here this isn't the only type of wave you can have I mean my definition is fairly general but it the definition is more general than just what I've drawn here for example you could have a sound wave a sound imagine you have a bunch of you know if you just look at the air if you just look at all of the molecules in the air they're just you know they have some density that looks something like that and I'll say I had some type of a membrane maybe it's a speaker that jolts this this left-hand side of the air so it just it just pushes so let me see if I can draw this so let's say I had some type of surface here all right let's say it's some type of surface here that just really quickly jolts that just moves in that direction and that just comes back so just similar to what I did here I go up and down but instead of doing that it just pushes the air and then pushes back so what's going to happen so right after it pushes it the air molecules that it pushes up against are going to jam together they're going to get compressed right here all of these air molecules that were right on the surface are going to get pushed next to all of these air molecules that are right there and then when it when it pushes back or when the membrane goes back you're going to have fewer air molecules here because you're going to have a low density here and then these guys they're all scrunched up together they're going to want to get away from each other they might even run into each other and so these guys are going to run into those guys who are going to run into the next guys and so on and so forth and when after these guys bump into those guys those guys are going to go back to where they were so essentially going to have this kind of this this disturbance is going to be one molecule bumping into or set of molecules compressing or bumping into its neighboring molecule so if you look at this at some future period in time all of a sudden this area might look normal let me clear it and draw it just the way I started off so this area might look normal this area will look normal but that compression of the particles might have reached right over here that compression of the particles might have reached right over there and not only that we saw that right after the compression you usually have a spirited area of low pressure so if I were to really draw this wave and actually if I were to if this membrane were to keep doing it over and over and over again so it kept going forward and back forward and back or right and left right and left but what you would have is a series of compressions the air would just have a series of compression so that's one compression you'd have another compression right there another compression right there and then in between the compressions the air is less dense the air is that's like this and what we've essentially just generated is a sound wave traveling through air so this right here is a sound wave and this type of wave where the direction of the disturbance is the same or along the same axis as the direction in which the wave is traveling the wave is traveling in that direction this is called a longitudinal wave so sound waves sound through air their longitudinal waves longitudinal Dental wave sometimes called a compression wave compression wave same thing compression wave because it's caused by compression our example of the string this is called a transverse wave this is called a transverse wave transverse because the disturbance the movement of the medium is going in a direction transverse to the or an axis that's transverse to the direction of our movement we're moving in that direction to the right but actually our wave is moving to the right but the actual medium is moving up and down our medium is moving up and down that's why this is called transverse while here the medium is moving left and right while the wave moves to the right so it's along the same axis so we're dealing with compressional or longitudinal now in the in this first example I just did one cycle I just wait I just jerked up down and back again and I created this one disturbance and we can call this when you just have do it once you can view this as a wave pulse as a wave pulse if I kept doing that if I just went up down back again up down back again and I kept doing it periodically over and over again then I will generate a periodic wave and my string would look something like this my string would look something like would look something like that well actually it would look something like something like that right there where that's kind of that's the disturbance generated from our first time that we that we moved this left-hand part of our string so this is right here is a periodic wave periodic wave and in the next video we're going to talk about a lot of the properties of periodic wave how the wavelength and its frequency and its period relate to its velocity and all of that but I'll leave that alone in this video but I just want to appreciate what I think it's kind of a you know it's a it's a concept that we use in everyday life oh it's a wave it's a sound wave and all of that but it's a fairly abstract notion when we talk about a wave we're really just pointing to a disturbance that's moving usually along a medium at least when you know we visualize it but not always but we're just pointing to this disturbance and the disturbance can take many forms it could take this kind of it could be a transverse disturbance if we're dealing with a string it could be a disturbance in terms of the density of air molecules in terms of a sound wave and there is a relation so if you wanted to just plot the density here by position you could you know if I were to mathematically represent this compression wave right here so let's say that this line represents just resting normal you know before the sound waves hits that's just your normal density if we were to plot the density it might look something like this so over here we have very high density over here we have very low density over here we have very high density and if you were to plot it it would look a lot like that transverse wave that transverse wave that I did with the rope at the beginning of this video and that's why they're even grouped together because mathematically even though a compression wave looks very different or you might visualize it or conceptualize it very different than a transverse wave mathematically they're essentially the same thing you have this quantity in this case it's the density of the air varying over time in this case it's the height or the position or how much you've your displacement from your resting position that's the quantity varying through time that's that's traveling that that disruption is traveling over the course of the medium that's why we call both of these things ways anyway I'll let you go here and the next video we'll talk a little bit more of the properties of periodic waves