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Current time:0:00Total duration:10:36

Video transcript

what we're going to do in this video is think about two wave sources but one of them is going to be stationary and the other one is going to be moving and just to have a concrete number it's moving at five meters per second to the right and we're going to think about is where are the crests of the wave that it's been releasing for the last three or four seconds so let's say they're in both cases they are releasing a wave so the velocity of the wave is going to be 10 meters per second you could visualize this maybe as a sound wave but sound and air moves much much much much faster than 10 meters per second but this will make the math work out easy especially relative to this guy who's moving to the right at 5 meters per second and that's the whole point to give you the intuition and make the math a little simple here and both of these guys are going to be the wave that they're emitting is it 10 meters per second and the period of the wave is going to be at 1 second per cycle and if the period is 1 second per cycle you take the inverse of that the frequency of the of the source I guess you could call it of the wave as it's being emitted is going to be the inverse of this the inverse of 1 is just 1 but one cycle one cycle per second if it takes a second for a cycle it's also in one second you're also going to see one cycle so one cycle per second so let's think about what's happening here so let's think about where let's say it emitted a crest of its wave exactly one second ago where is that crest going to be now let's think about the stationery character well in this guy emitted the crest one second ago it's moving outward so this is outward it's moving outward rade radially I need to give a direction if I'm giving a vector quantity so it's moving outward at 10 meters per second so if it emitted it one second ago it's going to be 10 meters radially outward from the source so maybe that is right over right over there it looks let me draw it a little bit neater like that let me draw it a little bit neater that's pretty good so that's where that crest will be now what about this guy where is the crest that this guy emitted one second ago well you might want to just draw a radius 10 meter around this guy as well but he wasn't here one second ago he was 5 meters to the left remember he's moving 5 meters per second to the right so 1 second ago he was 5 meters to the left so maybe that places him right over there so the the crest that he emitted 1 second ago isn't going to be or it's not going to be 10 meters from this guy it's going to be 10 meters radially outward from that guy so let me just copy and paste this right here so copy and paste and just put it right over there so this is where he is now that's where he was 1 second ago where he emitted this crest that has now traveled 10 meters away this is a little inexact so I could a little bit like that this is 5 meters that's 10 meters away but you get the general idea now let's keep going let's think about the crest that both of these guys emitted two seconds ago so this guy's been stationary the whole time if he emitted it two seconds ago it's traveling at 10 meters per second it's going to be 20 meters radially outward from the center from the source so it will be it will look something something like that I'm just drawing the crests of the waves if you think of a water pebble being dropped into pond these are just the high points on the on the wave that spreads radially outward from where the pebble was dropped now this guy once again you can't just draw a circle around this because he wasn't here two seconds ago he was right here he was right here two seconds ago one second ago he was five meters to the left a second before that he was five meters more to the left so that wave that he made it then is going to be 20 meters radial outward from this point and so let me just copy and paste this right here so copy and paste so the center isn't going to be that or that it's going to be that point where he was two seconds ago let's do this again let's do it again let me use pink so what about the crest that either of these sources emitted three seconds ago well do it would be thirty meters radially outward so another ten meters from the last one so it will be it will be out here it will be out there just like that this guy's been stationary the whole time but what about this guy well he wasn't here ten meter once a three seconds ago he was here right one second ago here two seconds ago there three seconds ago there so we're going to be thirty meters radially outward from this point so once again I can just copy and paste this right here so copy and paste and it should be centered around that point around that point right there now let's think a little bit about what what the perceived frequency of this wave would be for a couple of observers so we could put an observer here really anywhere around this guy we could put an observer right here and then we could put another observer right here now what's this guy going to perceive well every second he's getting a pulse being well there's a couple of things to think about first of all what is the wavelength of at least this wave right here well every second he's emitting a pulse so a second ago the pulse is out there would have traveled ten meters and then he emits another pulse so the pulses are going to be one second apart but since they travel ten meters in that one second they're also going to be ten meters apart so the wavelength in this case is going to be ten meters the distance between these crests are ten meters now what about this situation right here what depends on kind of what side whether the source is coming towards you or whether it's going away from you that's the situation with this guy in this when it's when it's moving towards you it's emitting a pulse so let's say it emitted a pulse right here and then it moves five meters to the right before emitting the next pulse so instead of them being ten meters apart in this case this guy has kind of closed the distance by five meters over here so these pulses are only going to be five meters apart so over here the wavelength is only five meters and you can see it visually this distance right here is half of this disk these are five meters apart and on the left-hand side if you're on the the side of the source that is open that the source is moving away from it would be ten meters but every second the source is also moving five more meters away from you so this wavelength right here this perceived wavelength right here is going to be fifteen meters it's 15 meters and we can see it visually that's the whole reason why I drew it this way now what's going to be the perceived frequencies for this well this guy you know he has one crest passing him right now it's going to take exactly one second for the next crest to get to him because there's traveling at 10 meters per second so he is going to perceive he is going to perceive one crest or one cycle per second or one a frequency of one Hertz which makes sense this is stationary they're both stationary relative to each other and we're also talking about classical physics we're not getting into relativity and all of that but the observed frequency is the exact frequency that was emitted by this guy right there now what about this situation well each of these crests are five meters apart for this guy you know if you imagine that this was some type of a train coming to towards this guy each of these crests are only five meters apart but they're traveling at 10 meters per second so how many crests are you going to see in a second we're going to see two of them this one's going to take half a second to reach you and then the next half a second this one's going to get to you or you could say this one's takes half a second to reach you then this one's going to take one second to reach you so you're going to see two so there's two ways to think of it you could say your period in this situation is one half of a second per cycle or you could invert it and you could say that the frequency observed we can put the observed frequency is going to be two cycles per second and already notice this guy's experiencing a higher frequency than this guy over here because these wave fronts or these crests are just passing by him more frequently because they were because this guy is moving in the same direction as this guy they are closer together now this guy's going to experience the opposite thing let's say that this crest is just passing him by how long will it take for the next crest to cover that meters well they're going at 10 meters per second it's going to be 1.5 seconds seconds per crest that's going to be the observed period for this guy you take the inverse of that that's 1.5 is three-halves it's two-thirds of a or you can say crest or 2/3 of a cycle per second so when the source is moving away from this observer the frequency or the perceived frequency is lower than the frequency of of the actual emitted wave when the source is moving towards the observer the frequency is higher this might seem something some type of bizarre thing but you've experienced before it's called the Doppler effect which you've probably heard of and that's exactly what you experience when you sit at you know at maybe a train crossing be careful not to sit too close and as a train is approaching you you notice it has a very say it has its horn going on it be very high-pitched and then right when it passes you and it starts moving away from you it starts it has a much lower pitch and that perceived pitch that's your that's your brain in your ears way of sensing frequency so when the train is coming towards you it's a high pitch high frequency when it's going away from you low pitch low frequency and hopefully drawing it out this way gives you a visual understanding of why that is why these these points on the cycle or these crests are closer together when it's moving in your direction and when they're farther apart when it's moving away from you and the next video we'll do this with more abstract numbers so we can actually figure out generalized formulas for relating the observed frequency with the emitted frequency