The Doppler Effect

by Jared Rovny
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00:02 A last thing to discuss with the sound chapter that we have going here is the Doppler Effect.

00:09 So what we have is a car which just went by and what this car is going to do, if you've ever heard any sort of vehicle driving by you making some sort of sound, you've probably heard the sort of sound that we just experienced.

00:22 The car driving by, it has a high-pitched sound and then a low-pitched sound.

00:26 It goes, 'wooom' like that.

00:27 So as it moves by, it's making a sort of weird sound and why in the world is this happening? We have a physical intuition for what sound is now.

00:35 We have these pressure waves and the movement through the air.

00:37 So how can we describe or how can we think of what's causing this change in the pitch of a sound.

00:44 It comes from something called the Doppler Effect.

00:46 So let's see how this works.

00:47 You have your car and maybe it's making some sort of noise.

00:50 It's honking or it's a siren or something like this.

00:52 The sound is going to spread out from the source of the sound, in this case your car.

00:58 As the sound spreads out, it's going to be the same in all directions if your car is not moving.

01:03 So it's just gonna keep going in this bigger and bigger circles as it moves outwards.

01:08 What this means is that no matter where you are, you're going to hear the same frequency and see the same wavelength of your sound.

01:15 Now, let's let our source move.

01:16 So if you have a car like this one, it creates some sound waves.

01:19 So literally, if you look at it, it would have some speaker and it's creating sound.

01:23 It's increasing and decreasing the pressure, increasing and decreasing and so we have a wave created as it moves.

01:29 We allow it to move a little bit, but look what happens.

01:33 The original wave that it made when it was first starting out has expanded.

01:38 So that's the bigger circle.

01:39 It's the original wave that's moving outwards still.

01:41 But the car is still making noise as it moves and so it's created a new sound wave.

01:46 That sound wave also for the same physical reasons will start moving outwards in a circle.

01:51 As the car moves, it keeps creating more and more sound as it goes while the original sound waves are simply expanding around whatever point they started at.

02:00 So look at what's happening with this car.

02:03 If we examine the wavelength of the sound on the left of the car or behind of the car, it has a longer wavelength, a longer distance between peaks and troughs of the pressure because the car is moving away from the creation of those pressure waves.

02:19 So somebody behind this car, somebody for whom the car is moving away would hear an increased wavelength which corresponds to a decreased frequency, a lower pitch and so as an object is moving away from you, you hear a lower pitch.

02:34 On the other hand, if something is moving towards you, you hear a decreased wavelength which corresponds to a higher frequency or a higher pitch.

02:42 So something's moving towards you, you hear a very high sound.

02:45 If something's moving away, you hear a very low sound because again you can just look at a picture like this and compare the wavelengths and therefore compare the frequencies and this explains the Doppler Effect, this sound difference that we hear because you know just from experience that if something is moving past you, it starts with a very high sound and then it moves to a very low sound.

03:05 It starts high and then goes low.

03:06 So I recommend you listen to some example of wavelengths or frequencies of some thing moving past or an ambulance driving by and listen for that, listen for the high frequencies and then moving towards the low frequencies as it goes by.

03:20 What we're going to do now is measure what those frequencies are.

03:24 So the Doppler Effect, measures again something that's moving.

03:28 So we call that a velocity of the source, whatever is creating the sound.

03:31 So a velocity of the source that's moving towards this person.

03:35 We have to be careful here because it's also possible that the person, the observer is also moving.

03:41 So we have to account for both motions, both different, a relative speeds here because the fact that the observer is moving could cause the same sort of effect to happen.

03:51 They could hear a different frequency because they would experience this pressure waves differently depending on how quickly they're encountering them.

03:58 So keeping both of these in mind, that we have a velocity of the source, a velocity of the observer, the person hearing the source of sound.

04:05 We have an equation for the new frequency, so that's the Doppler Equation here for the frequency.

04:10 The frequency of the sound that the observer will hear will be equal to the original frequency that was created at the car, for example, times its ratio.

04:20 So this term here, this ratio of this velocities tells us of how the frequency is shifted and so this is the key term here and what does it say? The velocity terms in this equation are v, the velocity of the sound itself plus or minus the velocity of the observer.

04:38 Where we use plus or minus because you might be moving forward away from the object or backwards towards the object, divided by the same sort of term, the velocity of the sound minus-plus the velocity of the source.

04:51 So why do use minus-plus here? Well, we have to be careful with the relative directions.

04:56 So if one person is moving away, while the source is moving towards him, we have to have a different sign for those velocities.

05:03 So whichever velocity convention you're using to represent forward for one, you would use to represent backwards for the other.

05:10 So just be careful with the signs here and make sure it makes sense that as a sanity check, something you can always do to make sure that you have the right equation is ask yourself what happens if both people are moving, both the source of the sound and the observer of the sound are moving.

05:23 In this case, what you should get by plugging in the same velocities for both of them is that you have no Doppler Shift because relative to each other, they don't know that either one is moving.

05:33 In other words, this person moving or the source moving towards the person is creating a higher pitch but the person is moving away and so experiences it at a lower rate and so you get no net effect.

05:44 Just using that sort of logic, you can always make sure that you get the signs correct in your Doppler equation.

05:51 It is very important to notice in this equation, you have very different sorts of v for velocity.

05:57 The velocity of the sound which is the v without any subscript in this equation is something that has nothing to do with the motion of either object and only depends on the medium that you're traveling through.

06:08 So be very careful with this in this equation.

06:10 Both the person who's observing the sound and the source of the sound can be moving but the velocity of the sound itself is not something we can change or edit or do anything with.

06:19 It just depends on the medium that the sound is traveling through or the medium that any wave which will include light is traveling through.

06:26 The observer and the source of velocities can also be negative and they can also be zero.

06:32 So again this has to do with the signs that we're using for the velocities and be very careful when you're using these signs again to make sure that the relative sign between the two is something appropriate to the Doppler shift which shouldn't occur if they're moving together at the same speed.

06:47 This summarizes our more complicated, may be more in depth chapter about sound and how to use sound both as standing waves and pipes as well as the source of the Doppler Effect.

06:57 So hopefully the sound chapter made sense.

06:59 It's possibly one of the more challenging concepts, so I encourage you to go over it, really go over some notes for this one. Try some practice problems.

07:06 See if it makes more sense.

07:07 Maybe even listen to the lecture again or at least a few key points of it and if you've done that and it, it makes sense to you with both the standing waves as well as the reasoning behind the Doppler Effect.

07:17 We're ready to move on to the other wave phenomenon which is Light.

07:20 Thanks for listening.

The lecture The Doppler Effect by Jared Rovny is from the course Sound.

Included Quiz Questions

1. It has a higher frequency
2. It has a higher wavelength
3. It has higher pressure
4. It has lower pressure
5. It moves faster
1. Move the source towards higher x or move the observer towards lower x
2. Move the source towards lower x or move the observer towards higher x
3. Move the source towards higher x or move the observer towards higher x
4. Move the source towards lower x or move the observer towards lower x
5. Move the source and observer away from each other
1. The velocity of sound will only depend on the medium
2. Increase the velocity of the observer
3. Increase the velocity of the source
4. Increase the relative velocity of the observer and source towards each other
5. Increase the relative velocity of the observer and source away from each other
1. The speed of sound towards the source
2. The speed of sound away from the source
3. Twice the speed of sound towards the source
4. Twice the speed of sound away from the source
5. This is never possible

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