Full transcript
0:00Now, this Doppler shift can be described
0:02by the following formula. And so, let's
0:04look at what some of the different terms
0:05mean. Remember, we've encountered lambda
0:07before, and that was the wavelength of
0:09the wave we're looking at.
0:11So, wavelength of a wave. In this case,
0:14this would be the wavelength we would
0:15expect to see.
0:18Now, this new symbol here, this delta,
0:19the triangle, means change in. So, in
0:22this case, change in wavelength. So,
0:25we're going to look at the wavelength we
0:26actually see versus the wavelength we
0:29expect to see. So, take the wavelength
0:32you
0:32would observe minus the wavelength you
0:36would expect to see, and you might get a
0:39positive or a negative.
0:40And that's part where if you're confused
0:43by that ever and are unsure which way to
0:45go, you can always figure out if it
0:46should be negative or positive later.
0:48So, we'll look at an example in a second
0:50to see what I mean. But just think of
0:52this as the change in wavelength. Now, C
0:55is the speed of light, which is a known
0:57quantity, approximately 300 million
0:59meters per second. And V is the velocity
1:03of the object. And this is the relative
1:05velocity if it's moving away or towards
1:08us. It might have other velocity that is
1:10perpendicular to our motion, but this
1:12formula wouldn't determine that.
1:14So,
1:15let's take a look at an example. And
1:17it's worth noting, by the way, your book
1:18does have other examples of the Doppler
1:20effect. You might want to check this
1:22out. It is a difficult formula to use,
1:24so it's worth seeing a few examples and
1:26trying a few.
1:27So,
1:29what do we got? We are told that the
1:31emission line of an object
1:34is originally supposed to be at 678.2
1:38nanometers. So, something's spitting out
1:40a wavelength we would expect to see at
1:42678.2 nanometers, but we actually
1:46observe it at 677.7
1:49nanometers.
1:51And because of this difference, we know
1:53that there must be relative motion
1:55between us.
1:56So, we're asked, "How fast is the object
1:58moving toward or away from us?
2:01Great. Now, if we wanted to, we could
2:02already determine whether it's moving
2:04away or toward from us, but let's try
2:06and let the math handle it first, and
2:08then talk more about that in a sec. So,
2:11first we need to know that this is the
2:13lambda we expect to see. So, that's our
2:16number going down on the bottom over
2:18here.
2:19The difference between them, again, we
2:21take this number, what we actually
2:23observe, minus this. So, what we're
2:26going to actually get is 0.5, but -0.5,
2:30cuz this number is bigger. So, this is
2:31going to be negative, and we ultimately
2:33want the velocity, so we're going to
2:34have to multiply both sides by C to
2:36bring it over. So,
2:38we see V equals, again, this formula. We
2:40multiplied both sides by C to bring it
2:42over, and then we plug in our numbers.
2:44C, again, we know, and then we've just
2:46determined what lambda and change in
2:48wavelength is, as well.
2:50Which we see, again, 3 * 10^8, and our
2:54Don't think this is subtraction, by the
2:56way. This is all multiplied. What we're
2:57going to do is take this number,
2:58multiply it by this, divide by that.
3:01And we ultimately get a negative
3:04velocity. And you should try plugging
3:05this in your calculator, by the way. Try
3:08doing this, and make sure you get the
3:10same answer as me. Because what you
3:12might need to do is put this part in
3:13brackets. What a lot of students will do
3:15by accident is take this and try to
3:18multiply it out, but what they end up
3:19doing is multiplying eight by this
3:22number. So,
3:24if you're ever finding that you're not
3:26getting quite right math, make sure to
3:28put some extra brackets around the
3:30numbers to separate them, and of course,
3:32also come see me. I can help show you
3:34how to use a calculator, and make sure
3:36it comes out properly. So,
3:38we got this number. This -221,000
3:43m/s.
3:44Now, remember,
3:46the negative
3:48is actually meaning something in this
3:50case. One thing we forgot to mention up
3:53here is that if we have a negative
3:56number, the negative means it's actually
3:59moving towards us. If we have a positive
4:01number, it means it's moving away.
4:04So, we've actually got our answer right
4:07here. It's moving at a roughly 221,000
4:10m/s towards us.
4:13Now, let's say you were confused by this
4:15delta.
4:17Didn't know which number should be
4:18subtracted and you accidentally used
4:200.5. And so, that would still give you
4:23the right velocity.
4:24This negative doesn't really matter in
4:26the calculation other than it ends up
4:28putting a negative here. If you ever are
4:30unsure, you can always just come up with
4:32a number and then look at the
4:34wavelengths. We expect to see 678.2.
4:39But, we see 677.7.
4:42Great. The main idea is this number,
4:44what we actually see is smaller than
4:46what we expect. The wavelength is
4:48smaller,
4:49meaning we're going to blue shift,
4:51meaning it's moving towards us. So, we
4:53don't need to worry about the negative
4:54if we don't want to.
4:56We can just figure out it's moving
4:58towards us or away from us by comparing
5:01what we see versus what we expect to
5:03see.
5:04If the number we see is smaller than we
5:06expect, it's moving towards us. If it's
5:08larger than we expect, it's moving away
5:11cuz that wavelength's being stretched
5:12out. Think back to that previous image
5:16where you can think it gets stretched
5:17out or compressed depending on its
5:19motion towards us.
5:21So, it's moving towards us in this case,
5:23which you get from the negative or from
5:25comparing these numbers.
5:28Now,
5:28what you might be asking yourself is,
5:31"Great, we expect to see a certain
5:34wavelength. How do we know?"
5:36I mean, this is a distant object. How do
5:38we know what we expect? Well, the thing
5:40is,
5:41remember those absorption spectrum?
5:44When we have this Doppler effect, the
5:46entire
5:47line set of lines gets shifted.
5:50So, like the analysis we're talking
5:52about before using spectrometers, we can
5:55still do, and we'd expect this right
5:58here. This is the element we don't know
6:00in a lab. But, if it's actually shifted
6:04towards the blue part of the spectrum,
6:05each and every single one of these lines
6:07is shifted the same amount. And so, we
6:09can clearly see this is a blueshift. We
6:13can compare the wavelength we expect
6:16versus the wavelength we
6:18get. And if it was moving away from us,
6:21we'd get a redshift. In this case, a
6:23very drastic redshift. And you can see
6:25once again, all of the lines are moved.
6:28So, we can still recognize the element
6:31and still use the analysis we had
6:33before. And it actually does shift the
6:35lines simply because it's moving
6:38relative to us. So, now, not only can we
6:41determine what this thing is made up of,
6:43but we can also determine if it's moving
6:45towards us or away from us. So, even
6:47more information just by studying the
6:50light this object gives off.