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:7:35

When the source and the wave move at the same velocity

Video transcript

in the last several videos we assume that the velocity of the source of the object that's emitting the wave we've assumed that that's less than the velocity of the wave and we saw what happens with the Doppler effect and all of that but what I want to do in this video is not make this assumption in particular let's see what happens at least at first to our formulas and then get a conceptual understanding let's see what happens when the velocity of the source is equal to the velocity of the wave so the first thing we might try to do is just apply this assumption this new assumption into the formulas that we had in the last video and those formulas were here these are the observed period and frequency for an observer that's kind of in the direction of the object and if we make this assumption that the velocity of the sound and the velocity of the source we're not necessarily dealing with sound waves although that might be an easy visualization for you that's tends to be how I visualize it but if what happens to these formulas when the velocity of the source is equal to the velocity of the wave well if these two quantities are equal up here you have something subtract the same thing from it this numerator right here becomes zero so it'll turn this whole thing into being zero so the period or the observed period will be zero which means you don't have to wait any time at all between successive crests that the that D that the entire waveform just gets infinitely bunched together so it's just you know just it's just kind of like one impulse and if we look at the frequency we can either look directly at the formula and you'll see well you have something divided by zero right here so you could say this is one over zero or you could just say that the frequency is one over the period and you get this thing that's undefined undefined but if you want to think about what does a frequency approach as the velocity of the source approaches the velocity of the wave if this thing is only a little bit less than that thing this is going to be a very very very small very very small positive number so when you divide these quantities by that very very very small positive number you're going to approach infinity so the frequency is going it's undefined at the speed at the velocity of the wave but it's going to approach infinity approach infinity it will approach infinity as the source approaches the sound as far as the source approaches the velocity of the wave not necessarily a sound wave I keep using sound wave just because that's how I tend to visualize things we'll talk in future videos specifically about sound waves and we'll touch on it a little bit in this video so what is this telling us does this make any sense and if you think about it at least into me you know it starts to make it starts to make sense just what you saw in the last couple of videos in the last couple of videos when something was moving slower than the speed of sound you had okay I am here now and then maybe and I'm about to eat to release the next crest if I go one period ago maybe I was right there and the crest that I had released at that time period maybe has traveled this far just like that if you go a period before that I would have been over there and the crest that I released then would have traveled that far we saw this in the last two videos and if you go the period before that I would have been there and the crest that I would have released would have been that far and this was the whole reason why the Doppler effect happens because the observer sitting right here let me do this in a separate color the observer sitting right here is going to experience these crests more frequently than an observer sitting out here because the wavelength gets compressed because every time this guy releases a new crest or a new cycle he is moved forward he has moved forward in the direction of this motion right here so let's think about what happens when he is exactly moving at the speed of the wave so let's say that the source is here now this is right where he is and he's right about to release a new crest so where was he at one period ago so let's say he was here one period ago and where is the crest that so one period ago he if he was if he's right going to release a crest or cycle right now one period ago he would he released another cycle and where has that cycle gone well we're assuming that the wave is traveling at the same velocity as this guy but it's going radially outward so whatever he released then it will have traveled at the same velocity as himself so it will got it will have gotten this far right he released it one period ago and that's where he was one period ago over the course of the next period he traveled there and so did the wave the wave also traveled there now where was this character two periods ago two period when I talk about the period I'm talking about the actual period of the wave every period or kind of how long does it take between similar points in the cycle and I like to think of them as the crest in the cycle so two periods ago he was here and he released a you could imagine a pulse or crest and where will that be now well that will have traveled as far as he did he traveled that far and so will the pulse that he released it will have traveled fact you have to make it a little bit more symmetric it will have traveled that far so it will have traveled that far it will have travelled that far then if you go three periods ago I think you get the idea if you go three periods ago he was here and he released he released a pulse then or a crest or or or a cycle of the wave and where will that be now well it will have traveled as fast as he's gotten so it will have gotten this far so it will have gotten that far of course it's traveling that velocity in every direction radially outward now think about the situation for the observer think in particular think about the observer who's sitting right here let's say he's just out of the way so that this thing doesn't run into him and kill him and whatever else but he's just out of the way just enough to experience the sound but not be directly collide with this object that's emitting the what I shouldn't say sound emitting the wave I want to be general right here we're not assuming that this is a sound wave what's he going to experience well he's not going to well if we assume this is a sound wave he's not going to hear anything until the thing passes right there and right when the thing passes it has all of the sound that it generated coming with it at exactly that moment in time instead of hearing things instead of hearing things periodically all of the wave fronts smack this guy all at once and perceptually instead of hearing a pitch because you're hearing something periodic because you're just going to hear a big thump because all of that sound energy is getting to you at the same time you're just going to hear a thump because it's no longer really a frequency all of the energy is coming to you at the same time and we're talking about sound specifically and especially when you are transonic which means you're around the speed of sound or parts of you are are above or below the speed of sound and you move into supersonic speeds that's what people relate to the sonic boom and we're going to talk a little bit more about that in the next video and Mach numbers all of that because I just find all of that fascinating but I think this is intuitive because when you look at this all of the way everything is just reaching you at exactly the same time and you know that this was the case it sound waves but it would be true of any type of waves