The Doppler Effect - Video Tutorials & Practice Problems
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The Doppler Effect
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Hey guys, if you've ever stood on the side of a road while an ambulance blaring its silent siren has moved past you, you might have noticed that the sound changes once it passes by, it sounds like. And that's what the Doppler effect is. So in the studio, I'm gonna show you what causes the Doppler effect. But more importantly, I'm gonna show you the one equation that you need to solve any kind of problem that deals with it. Let's check this out here. Basically what the Doppler effect is is it's a shift in the frequency that you hear from the frequency of the sound source. So we call the frequency you hear F listener or fl and the frequency of the sound source F sound or FS. So it's not as if the ambulance actually produces a different sound as it passes by. What happens is that the frequency you hear gets shifted. So we call it sometimes a Doppler shift. Now, this Doppler effect happens whenever the sound source, meaning the siren or the sound listener, meaning you are moving relative to each other. So you have to have some relative motion of the two objects in order for you have the Doppler shift. Now, I'm gonna get back to the equation in just a second here. But I wanna show you sort of visually what's going on here and why the Doppler effect gets produced. So if there's no relative motion, there's no Doppler effect. So if you are standing on the side of the road, your velocity of the listener is gonna be zero. And if the ambulance is parked on the side of the road, the velocity of the sound source is gonna be zero. So what happens is if this sound wave or sorry, if this ambulance is producing waves at a rate of five Hertz. So it's five waves per second, then what happens is that these waves are traveling towards you at the speed of sound. The ambulance is producing five waves every second. Then what happens is that later on five waves are gonna pass through you every second. So if nothing's moving, what's gonna happen is that the frequency that you hear is gonna be equal to the frequency of the sound source. So you're just gonna hear five Hertz, right? Nothing's nothing gets shifted, nothing like that because five waves are gonna pass through you. Now, things get a little bit trickier whenever you do have some relative motion. And there's actually four different scenarios, you could have you the listener moving towards or away from the source or the source that's moving towards or away from you. So I'm gonna show you these really, we're gonna see that there's only actually two scenarios. So now imagine that you're actually moving running towards the sound source with some VL and the sound source is basically just standing still. What happens is that the ambulance is still producing five waves a second, still producing a sound of five Hertz. So what happens here though is that if you're moving towards the sound source, you're gonna be able to cover more waves every second, you're gonna be able to move through more waves as they're passing by you. So in general, what happens is you're gonna hear something that's greater than five Hertz, you're gonna hear basically more waves per second. The exact same thing happen if the ambulance were actually moving towards you with some sound source like this, basically, what happens is that these waves sort of get crammed up together in front of the sound source and they sort of get stretched out or elongated behind it. But the effect is the same, you're gonna hear more of these waves every second because the thing is actually moving towards you. So you're gonna hear something that's greater than five Hertz. So generally, what happens is that the listener on the sound source are moving towards each other, then the frequency you hear is going to be greater than the frequency of the source. That's the general rule. Now, if you reverse everything, it's basically opposite if you're moving to away from this source or if the source is moving away from you, the exact opposite happens, basically, you're gonna hear less waves per second. So you're gonna hear something that's less than five hertz in both of these situations. So, and if the listener source are moving away from each other, you're gonna hear less waves per second and the frequency that you hear is gonna be less than the source. So that's why, what happens is that when the ambulance is moving towards you, you're gonna hear a higher pitch or a higher frequency, it's gonna sound like e and then once it passes you, it's gonna be moving away from you and you're gonna hear something that is a lower frequency. So it sounds like as it passes by. So let me show you the equation real quick. Remember it's a shift between FL and FS and what goes inside here is really just a ratio. It's gonna be V plus VL over V plus vs. Now, unfortunately, there are three vs in the side of this equation. So I'm gonna go through them very quickly. This V here with no subscripts is gonna be the speed of sound. It's always gonna be positive to 343 m per second. No matter what this VL here is gonna be the velocity of the listener which is you and this uh vs here is gonna be the velocity of the source basically the velocity of the siren or the ambulance or whatever it is, right? So that's just the one equation that works for any kind of these situations here. Let's go ahead and take a look at our practice problem here. So we have the alarm of a car that's at rest. It produces sound waves of frequency 550. So this is actually the frequency that is produced by the sound source. It's gonna be 550. Now you're on a motorcycle and you're traveling directly towards it. So what happens here is you have this FS but you're gonna be moving towards this sound horse sound source with some VL and you're hearing an observed frequency of 600. So this is the frequency that you're actually hearing. So this is FL at 600. So we wanna calculate how fast must you be traveling? All right. So that's basically gonna be this VL over here. We have the velocity of the sound source, but remember the car is actually gonna be at rest. So this velocity of the sound source is actually gonna be zero. All right. So basically, now let's go ahead and take a look at our uh equation. So we have this equation here. This is FL equals V plus VL over V plus vs and this is F times FS. So let's go through each one of our variables here. So I've got FL right. That's just the uh the 6, 600 now, I've got my V because it's always gonna be positive 343. What about this VL? That's actually what I'm looking for here. We also know that vs is gonna be zero, so we just can cancel that out. And we also have what the frequency of the sound source is. So you have one unknown. The problem here is that if you'll notice what happens is this ambulance produces sound waves and remember these sound waves travel at the speed of sound that's going towards the listener towards you. So what happens is we have these two arrows that are actually pointing in different directions. So in these kinds of problems, remember a velocity is a vector, we're gonna have to establish a direction of positive here. And basically, here is the rule. The rule is that the direction of positive is always going to be from the listener to the source. So what happens here is that this is the listener and this is the source. So the direction of positive is always gonna be from L to s from listener to source. So here is our direction of positive. And what that means is that this VL is actually going to be positive. You're always going to write it like this. But depending on uh your sign, you actually might have to pick up a ne a negative sign if that happens. All right. So let's take a look here. So we're gonna plug in some numbers, our fl is 600 this equals and 343. Now what happens is, remember this 343 is always going to be positive even though the direction of positive is this way and your velocity of the speed of sound moves to the right these sound waves, you're still gonna actually write the 343 as positive. All right. So we have 343 plus VL and then we're gonna divide this by 343 and now we're gonna multiply this by 550. So let's just go ahead and move this 550 over to the other side. Once you divide this 550 you're gonna get 1.091 which equals 343 plus VL divided by 343. So what happens is when you move this 343 up over here, you're gonna get 374.2 equals 343 minus V or sorry, plus VL. All right. So all we have to do is just move this 343 over, we're gonna get 374 points two minus 343. Uh And this equals VL and if you go ahead and work this out, you're gonna get 31.2 m per second. So that is the speed that you have while you are traveling towards the sound source. All right. So that's if there's one guys, let me know if you have any questions.
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