[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.87,0:00:04.17,Default,,0000,0000,0000,,I've got this source of a wave\Nright here that's moving to
Dialogue: 0,0:00:04.17,0:00:06.15,Default,,0000,0000,0000,,the right at some velocity.
Dialogue: 0,0:00:06.15,0:00:14.51,Default,,0000,0000,0000,,So let's just say that the\Nvelocity of the source-- let's
Dialogue: 0,0:00:14.51,0:00:19.46,Default,,0000,0000,0000,,call it v sub s to the right--\Nso we're really going to do
Dialogue: 0,0:00:19.46,0:00:21.18,Default,,0000,0000,0000,,what we do in the last video,\Nbut we're going to do it in
Dialogue: 0,0:00:21.18,0:00:23.63,Default,,0000,0000,0000,,more abstract terms so we can\Ncome up with a generalized
Dialogue: 0,0:00:23.63,0:00:26.16,Default,,0000,0000,0000,,formula for the observed\Nfrequency.
Dialogue: 0,0:00:26.16,0:00:30.19,Default,,0000,0000,0000,,So that's how fast he's moving\Nto the right, and he's
Dialogue: 0,0:00:30.19,0:00:35.40,Default,,0000,0000,0000,,emitting a wave. Let's say the\Nwave that he's emitting-- so
Dialogue: 0,0:00:35.40,0:00:40.93,Default,,0000,0000,0000,,the velocity of wave--\Nlet's call that v
Dialogue: 0,0:00:40.93,0:00:43.27,Default,,0000,0000,0000,,sub w radially outward.
Dialogue: 0,0:00:43.27,0:00:45.51,Default,,0000,0000,0000,,We've got to give a magnitude\Nand a direction.
Dialogue: 0,0:00:45.51,0:00:46.76,Default,,0000,0000,0000,,So radially outward.
Dialogue: 0,0:00:50.07,0:00:53.66,Default,,0000,0000,0000,,That's the velocity of the wave,\Nand that wave is going
Dialogue: 0,0:00:53.66,0:00:55.95,Default,,0000,0000,0000,,to have a period and a\Nfrequency, but it's going to
Dialogue: 0,0:00:55.95,0:00:58.55,Default,,0000,0000,0000,,have a period and a frequency\Nassociated from the point of
Dialogue: 0,0:00:58.55,0:01:00.63,Default,,0000,0000,0000,,view of the source.
Dialogue: 0,0:01:00.63,0:01:01.52,Default,,0000,0000,0000,,And we're going to\Ndo everything.
Dialogue: 0,0:01:01.52,0:01:02.84,Default,,0000,0000,0000,,This is all classical\Nmechanics.
Dialogue: 0,0:01:02.84,0:01:04.96,Default,,0000,0000,0000,,We're not going to be talking\Nabout relativistic speed, so
Dialogue: 0,0:01:04.96,0:01:07.58,Default,,0000,0000,0000,,we don't have to worry about all\Nof the strange things that
Dialogue: 0,0:01:07.58,0:01:10.58,Default,,0000,0000,0000,,happen as things approach\Nthe speed of light.
Dialogue: 0,0:01:10.58,0:01:15.67,Default,,0000,0000,0000,,So let's just say it has\Nsome period of-- let me
Dialogue: 0,0:01:15.67,0:01:17.13,Default,,0000,0000,0000,,write it this way.
Dialogue: 0,0:01:17.13,0:01:22.22,Default,,0000,0000,0000,,The source period, which is the\Nperiod of the wave from
Dialogue: 0,0:01:22.22,0:01:26.89,Default,,0000,0000,0000,,the perspective of the source,\Nso the source period, we'll
Dialogue: 0,0:01:26.89,0:01:31.85,Default,,0000,0000,0000,,call it t sub source, And the\Nsource frequency, which would
Dialogue: 0,0:01:31.85,0:01:34.40,Default,,0000,0000,0000,,just be-- we've learned,\Nhopefully it's intuitive now--
Dialogue: 0,0:01:34.40,0:01:35.90,Default,,0000,0000,0000,,would be the inverse of this.
Dialogue: 0,0:01:35.90,0:01:42.79,Default,,0000,0000,0000,,So the source frequency would\Nbe-- we'll call it f sub s.
Dialogue: 0,0:01:42.79,0:01:44.96,Default,,0000,0000,0000,,And these two things are the\Ninverse of each other.
Dialogue: 0,0:01:44.96,0:01:47.30,Default,,0000,0000,0000,,The inverse of the period\Nof a wave is its
Dialogue: 0,0:01:47.30,0:01:49.06,Default,,0000,0000,0000,,frequency, vice versa.
Dialogue: 0,0:01:49.06,0:01:52.01,Default,,0000,0000,0000,,So let's think about what's\Ngoing to happen.
Dialogue: 0,0:01:52.01,0:01:56.93,Default,,0000,0000,0000,,Let's say at time equal zero,\Nhe emits that first crest,
Dialogue: 0,0:01:56.93,0:01:59.43,Default,,0000,0000,0000,,that first pulse, so he's\Njust emitted it.
Dialogue: 0,0:01:59.43,0:02:01.54,Default,,0000,0000,0000,,You can't even see it because\Nit just got emitted.
Dialogue: 0,0:02:01.54,0:02:05.02,Default,,0000,0000,0000,,And now let's fast forward\Nt seconds.
Dialogue: 0,0:02:05.02,0:02:07.70,Default,,0000,0000,0000,,Let's say that this is in\Nseconds, so every t seconds,
Dialogue: 0,0:02:07.70,0:02:09.41,Default,,0000,0000,0000,,it emits a new pulse.
Dialogue: 0,0:02:09.41,0:02:11.97,Default,,0000,0000,0000,,First of all, where is\Nthat first pulse
Dialogue: 0,0:02:11.97,0:02:14.80,Default,,0000,0000,0000,,after t sub s seconds?
Dialogue: 0,0:02:14.80,0:02:18.17,Default,,0000,0000,0000,,Well, you multiply the velocity\Nof that first pulse
Dialogue: 0,0:02:18.17,0:02:19.65,Default,,0000,0000,0000,,times the time.
Dialogue: 0,0:02:19.65,0:02:22.78,Default,,0000,0000,0000,,Velocity times time is going\Nto give you a distance.
Dialogue: 0,0:02:22.78,0:02:24.20,Default,,0000,0000,0000,,If you don't believe me, I'll\Nshow you an example.
Dialogue: 0,0:02:24.20,0:02:27.98,Default,,0000,0000,0000,,If I tell you the velocity is 5\Nmeters per second, and let's
Dialogue: 0,0:02:27.98,0:02:30.85,Default,,0000,0000,0000,,say that this period is 2\Nseconds, that's going to give
Dialogue: 0,0:02:30.85,0:02:32.34,Default,,0000,0000,0000,,you 10 meters.
Dialogue: 0,0:02:32.34,0:02:34.58,Default,,0000,0000,0000,,The seconds cancel out.
Dialogue: 0,0:02:34.58,0:02:38.23,Default,,0000,0000,0000,,So to figure out how far that\Nwave will have gone after t
Dialogue: 0,0:02:38.23,0:02:42.09,Default,,0000,0000,0000,,sub s seconds, you just multiply\Nt sub s times the
Dialogue: 0,0:02:42.09,0:02:43.83,Default,,0000,0000,0000,,velocity of the wave.
Dialogue: 0,0:02:43.83,0:02:46.16,Default,,0000,0000,0000,,And let's say it's\Ngotten over here.
Dialogue: 0,0:02:46.16,0:02:47.96,Default,,0000,0000,0000,,It's radially outward.
Dialogue: 0,0:02:47.96,0:02:50.08,Default,,0000,0000,0000,,So, I'll draw it radially\Noutward.
Dialogue: 0,0:02:50.08,0:02:53.69,Default,,0000,0000,0000,,That's my best attempt\Nat a circle.
Dialogue: 0,0:02:53.69,0:03:00.08,Default,,0000,0000,0000,,And this distance right here,\Nthis radius right there, that
Dialogue: 0,0:03:00.08,0:03:03.14,Default,,0000,0000,0000,,is equal to velocity\Ntimes time.
Dialogue: 0,0:03:03.14,0:03:08.78,Default,,0000,0000,0000,,The velocity of that first\Npulse, v sub w, that's
Dialogue: 0,0:03:08.78,0:03:09.51,Default,,0000,0000,0000,,actually the speed.
Dialogue: 0,0:03:09.51,0:03:11.63,Default,,0000,0000,0000,,I'm saying it's v sub\Nw radially outward.
Dialogue: 0,0:03:11.63,0:03:12.80,Default,,0000,0000,0000,,This isn't a vector quantity.
Dialogue: 0,0:03:12.80,0:03:14.75,Default,,0000,0000,0000,,This is just a number\Nyou can imagine.
Dialogue: 0,0:03:14.75,0:03:19.45,Default,,0000,0000,0000,,v sub w times the period,\Ntimes t of s.
Dialogue: 0,0:03:22.10,0:03:23.78,Default,,0000,0000,0000,,I know it's abstract, but just\Nthink, this is just the
Dialogue: 0,0:03:23.78,0:03:25.30,Default,,0000,0000,0000,,distance times the time.
Dialogue: 0,0:03:25.30,0:03:29.33,Default,,0000,0000,0000,,If this was moving at 10 meters\Nper second and if the
Dialogue: 0,0:03:29.33,0:03:31.19,Default,,0000,0000,0000,,period is 2 seconds,\Nthis is how far.
Dialogue: 0,0:03:31.19,0:03:34.52,Default,,0000,0000,0000,,It will have gone 10 meters\Nafter 2 seconds.
Dialogue: 0,0:03:34.52,0:03:36.64,Default,,0000,0000,0000,,Now, this thing we said\Nat the beginning of
Dialogue: 0,0:03:36.64,0:03:38.10,Default,,0000,0000,0000,,the video is moving.
Dialogue: 0,0:03:38.10,0:03:40.41,Default,,0000,0000,0000,,So although this is radially\Noutward from the point at
Dialogue: 0,0:03:40.41,0:03:43.34,Default,,0000,0000,0000,,which it was emitted, this thing\Nisn't standing still.
Dialogue: 0,0:03:43.34,0:03:44.72,Default,,0000,0000,0000,,We saw this in the last video.
Dialogue: 0,0:03:44.72,0:03:46.69,Default,,0000,0000,0000,,This thing has also moved.
Dialogue: 0,0:03:46.69,0:03:47.54,Default,,0000,0000,0000,,How far?
Dialogue: 0,0:03:47.54,0:03:48.70,Default,,0000,0000,0000,,Well, we do the same thing.
Dialogue: 0,0:03:48.70,0:03:52.33,Default,,0000,0000,0000,,We multiply its velocity times\Nthe same number of time.
Dialogue: 0,0:03:52.33,0:03:55.77,Default,,0000,0000,0000,,Remember, we're saying what does\Nthis look like after t
Dialogue: 0,0:03:55.77,0:03:59.23,Default,,0000,0000,0000,,sub s seconds, or some period\Nof time t sub s.
Dialogue: 0,0:03:59.23,0:04:01.13,Default,,0000,0000,0000,,Well, this thing is moving\Nto the right.
Dialogue: 0,0:04:01.13,0:04:02.66,Default,,0000,0000,0000,,Let's say it's here.
Dialogue: 0,0:04:02.66,0:04:05.57,Default,,0000,0000,0000,,Let's say it's moved\Nright over here.
Dialogue: 0,0:04:05.57,0:04:08.47,Default,,0000,0000,0000,,In this video, we're assuming\Nthat the velocity of our
Dialogue: 0,0:04:08.47,0:04:12.44,Default,,0000,0000,0000,,source is strictly less than the\Nvelocity of the wave. Some
Dialogue: 0,0:04:12.44,0:04:14.75,Default,,0000,0000,0000,,pretty interesting things happen\Nright when they're
Dialogue: 0,0:04:14.75,0:04:16.89,Default,,0000,0000,0000,,equal, and, obviously, when\Nit goes the other way.
Dialogue: 0,0:04:16.89,0:04:18.86,Default,,0000,0000,0000,,But we're going to assume that\Nit's strictly less than.
Dialogue: 0,0:04:18.86,0:04:23.15,Default,,0000,0000,0000,,The source is traveling slower\Nthan the actual wave.
Dialogue: 0,0:04:23.15,0:04:24.29,Default,,0000,0000,0000,,But what is this distance?
Dialogue: 0,0:04:24.29,0:04:25.98,Default,,0000,0000,0000,,Remember, we're talking\Nabout-- let me do it
Dialogue: 0,0:04:25.98,0:04:27.55,Default,,0000,0000,0000,,in orange as well.
Dialogue: 0,0:04:27.55,0:04:31.65,Default,,0000,0000,0000,,This orange reality is what's\Nhappened after t sub s
Dialogue: 0,0:04:31.65,0:04:33.16,Default,,0000,0000,0000,,seconds, you can say.
Dialogue: 0,0:04:33.16,0:04:35.36,Default,,0000,0000,0000,,So this distance right here.
Dialogue: 0,0:04:35.36,0:04:38.39,Default,,0000,0000,0000,,That distance right there--\NI'll do it in a different
Dialogue: 0,0:04:38.39,0:04:41.54,Default,,0000,0000,0000,,color-- is going to be the\Nvelocity of the source.
Dialogue: 0,0:04:41.54,0:04:46.35,Default,,0000,0000,0000,,It's going to be v sub\Ns times the amount of
Dialogue: 0,0:04:46.35,0:04:47.19,Default,,0000,0000,0000,,time that's gone by.
Dialogue: 0,0:04:47.19,0:04:49.34,Default,,0000,0000,0000,,And I said at the beginning,\Nthat amount of time is the
Dialogue: 0,0:04:49.34,0:04:51.48,Default,,0000,0000,0000,,period of the wave. That's\Nthe time in question.
Dialogue: 0,0:04:51.48,0:04:54.34,Default,,0000,0000,0000,,So period of the wave t sub s.
Dialogue: 0,0:04:54.34,0:04:57.95,Default,,0000,0000,0000,,So after one period of the wave,\Nif that's 5 seconds,
Dialogue: 0,0:04:57.95,0:05:00.91,Default,,0000,0000,0000,,then we'll say, after 5 seconds,\Nthe source has moved
Dialogue: 0,0:05:00.91,0:05:07.80,Default,,0000,0000,0000,,this far, v sub s times t sub s,\Nand that first crest of our
Dialogue: 0,0:05:07.80,0:05:12.30,Default,,0000,0000,0000,,wave has moved that far,\NV sub w times t sub s.
Dialogue: 0,0:05:12.30,0:05:14.30,Default,,0000,0000,0000,,Now, the time that we're talking\Nabout, that's the
Dialogue: 0,0:05:14.30,0:05:16.27,Default,,0000,0000,0000,,period of the wave\Nbeing emitted.
Dialogue: 0,0:05:16.27,0:05:19.81,Default,,0000,0000,0000,,So exactly after that amount of\Ntime, this guy is ready to
Dialogue: 0,0:05:19.81,0:05:21.96,Default,,0000,0000,0000,,emit the next crest.\NHe has gone
Dialogue: 0,0:05:21.96,0:05:23.50,Default,,0000,0000,0000,,through exactly one cycle.
Dialogue: 0,0:05:23.50,0:05:27.39,Default,,0000,0000,0000,,So he is going to emit\Nsomething right now.
Dialogue: 0,0:05:27.39,0:05:30.68,Default,,0000,0000,0000,,So it's just getting emitted\Nright at that point.
Dialogue: 0,0:05:30.68,0:05:33.76,Default,,0000,0000,0000,,So what is the distance between\Nthe crest that he
Dialogue: 0,0:05:33.76,0:05:37.99,Default,,0000,0000,0000,,emitted t sub s seconds ago or\Nhours ago or microseconds ago,
Dialogue: 0,0:05:37.99,0:05:38.73,Default,,0000,0000,0000,,we don't know.
Dialogue: 0,0:05:38.73,0:05:41.65,Default,,0000,0000,0000,,What's the distance between this\Ncrest and the one that
Dialogue: 0,0:05:41.65,0:05:43.21,Default,,0000,0000,0000,,he's just emitting?
Dialogue: 0,0:05:43.21,0:05:45.60,Default,,0000,0000,0000,,Well, they're going to move at\Nthe same velocity, but this
Dialogue: 0,0:05:45.60,0:05:48.81,Default,,0000,0000,0000,,guy is already out here, while\Nthis guy is starting off from
Dialogue: 0,0:05:48.81,0:05:50.26,Default,,0000,0000,0000,,the source's position.
Dialogue: 0,0:05:50.26,0:05:52.53,Default,,0000,0000,0000,,So the difference in their\Ndistance, at least when you
Dialogue: 0,0:05:52.53,0:05:54.63,Default,,0000,0000,0000,,look at it this way, is the\Ndistance between the source
Dialogue: 0,0:05:54.63,0:05:56.67,Default,,0000,0000,0000,,here and this crest.
Dialogue: 0,0:05:56.67,0:05:59.74,Default,,0000,0000,0000,,So what is this distance\Nright here?
Dialogue: 0,0:05:59.74,0:06:02.79,Default,,0000,0000,0000,,What is that distance\Nright there?
Dialogue: 0,0:06:02.79,0:06:07.27,Default,,0000,0000,0000,,Well, this whole radial\Ndistance, we already said,
Dialogue: 0,0:06:07.27,0:06:12.09,Default,,0000,0000,0000,,this whole radial distance is\Nv sub w, the velocity of the
Dialogue: 0,0:06:12.09,0:06:16.44,Default,,0000,0000,0000,,wave, times the period of the\Nwave from the perspective of
Dialogue: 0,0:06:16.44,0:06:19.17,Default,,0000,0000,0000,,the source, and we're going to\Nsubtract out how far the
Dialogue: 0,0:06:19.17,0:06:20.54,Default,,0000,0000,0000,,source itself has moved.
Dialogue: 0,0:06:20.54,0:06:23.35,Default,,0000,0000,0000,,The source has moved in the\Ndirection, in this case, if
Dialogue: 0,0:06:23.35,0:06:24.91,Default,,0000,0000,0000,,we're looking at it from\Nthis point of view,
Dialogue: 0,0:06:24.91,0:06:27.05,Default,,0000,0000,0000,,of that wave front.
Dialogue: 0,0:06:27.05,0:06:33.14,Default,,0000,0000,0000,,So it's going to be minus v\Nsub s, the velocity of the
Dialogue: 0,0:06:33.14,0:06:38.99,Default,,0000,0000,0000,,source, times the period of the\Nwave from the perspective
Dialogue: 0,0:06:38.99,0:06:40.34,Default,,0000,0000,0000,,of the source.
Dialogue: 0,0:06:40.34,0:06:41.78,Default,,0000,0000,0000,,So let me ask you a question.
Dialogue: 0,0:06:41.78,0:06:44.90,Default,,0000,0000,0000,,If you're sitting right here, if\Nyou're the observer, you're
Dialogue: 0,0:06:44.90,0:06:49.73,Default,,0000,0000,0000,,this guy right here, you're\Nsitting right over there, and
Dialogue: 0,0:06:49.73,0:06:52.68,Default,,0000,0000,0000,,you've just had that first\Ncrest, at that exact moment
Dialogue: 0,0:06:52.68,0:06:56.19,Default,,0000,0000,0000,,that first crest has passed you\Nby, how long are you going
Dialogue: 0,0:06:56.19,0:06:58.72,Default,,0000,0000,0000,,to have to wait for\Nthe next crest?
Dialogue: 0,0:06:58.72,0:07:01.52,Default,,0000,0000,0000,,How long until this one that\Nthis guy's emitting right now
Dialogue: 0,0:07:01.52,0:07:03.01,Default,,0000,0000,0000,,is going to pass you by?
Dialogue: 0,0:07:03.01,0:07:04.92,Default,,0000,0000,0000,,Well, it's going to have\Nto cover this distance.
Dialogue: 0,0:07:04.92,0:07:06.75,Default,,0000,0000,0000,,It's going to have to\Ncover that distance.
Dialogue: 0,0:07:06.75,0:07:07.65,Default,,0000,0000,0000,,Let me write this down.
Dialogue: 0,0:07:07.65,0:07:10.58,Default,,0000,0000,0000,,So the question I'm asking is\Nwhat is the period from the
Dialogue: 0,0:07:10.58,0:07:14.06,Default,,0000,0000,0000,,point of view of this observer\Nthat's right in the direction
Dialogue: 0,0:07:14.06,0:07:15.32,Default,,0000,0000,0000,,of the movement of the source?
Dialogue: 0,0:07:15.32,0:07:19.66,Default,,0000,0000,0000,,So the period from the point\Nof view of the observer is
Dialogue: 0,0:07:19.66,0:07:22.18,Default,,0000,0000,0000,,going to be equal to the\Ndistance that the next pulse
Dialogue: 0,0:07:22.18,0:07:25.24,Default,,0000,0000,0000,,has to travel, which is that\Nbusiness up there.
Dialogue: 0,0:07:25.24,0:07:26.90,Default,,0000,0000,0000,,So let me copy and paste that.
Dialogue: 0,0:07:30.26,0:07:32.39,Default,,0000,0000,0000,,So it's going to be that.
Dialogue: 0,0:07:32.39,0:07:33.15,Default,,0000,0000,0000,,Let me get rid of that.
Dialogue: 0,0:07:33.15,0:07:35.69,Default,,0000,0000,0000,,It shouldn't look like an equal\Nsign, so I can delete
Dialogue: 0,0:07:35.69,0:07:36.54,Default,,0000,0000,0000,,that right over there.
Dialogue: 0,0:07:36.54,0:07:39.07,Default,,0000,0000,0000,,Or a negative sign.
Dialogue: 0,0:07:39.07,0:07:41.34,Default,,0000,0000,0000,,So it's going to be this\Ndistance that the next pulse
Dialogue: 0,0:07:41.34,0:07:42.84,Default,,0000,0000,0000,,is going to travel, that one\Nthat's going to be emitted
Dialogue: 0,0:07:42.84,0:07:46.26,Default,,0000,0000,0000,,right at that moment, divided by\Nthe speed of that pulse, or
Dialogue: 0,0:07:46.26,0:07:49.31,Default,,0000,0000,0000,,the speed of the wave, or the\Nvelocity the wave, and we know
Dialogue: 0,0:07:49.31,0:07:50.40,Default,,0000,0000,0000,,what that is.
Dialogue: 0,0:07:50.40,0:07:52.56,Default,,0000,0000,0000,,That is v sub w.
Dialogue: 0,0:07:58.68,0:08:01.60,Default,,0000,0000,0000,,Now this gives us the period\Nof the observation.
Dialogue: 0,0:08:01.60,0:08:01.77,Default,,0000,0000,0000,,Now.
Dialogue: 0,0:08:01.77,0:08:03.85,Default,,0000,0000,0000,,If we wanted the frequency-- and\Nwe can manipulate this a
Dialogue: 0,0:08:03.85,0:08:04.19,Default,,0000,0000,0000,,little bit.
Dialogue: 0,0:08:04.19,0:08:05.98,Default,,0000,0000,0000,,Let's do that a little bit.
Dialogue: 0,0:08:05.98,0:08:08.94,Default,,0000,0000,0000,,So we can also write this.
Dialogue: 0,0:08:08.94,0:08:12.39,Default,,0000,0000,0000,,We could factor out the\Nperiod of the source.
Dialogue: 0,0:08:12.39,0:08:14.63,Default,,0000,0000,0000,,So t sub s we could\Nfactor out.
Dialogue: 0,0:08:14.63,0:08:20.44,Default,,0000,0000,0000,,So it becomes t sub s times the\Nvelocity of the wave minus
Dialogue: 0,0:08:20.44,0:08:26.69,Default,,0000,0000,0000,,the velocity of the source, all\Nof that over the velocity
Dialogue: 0,0:08:26.69,0:08:30.23,Default,,0000,0000,0000,,of the wave. And so just like\Nthat, we've gotten our formula
Dialogue: 0,0:08:30.23,0:08:33.31,Default,,0000,0000,0000,,for the observed period for this\Nobserver who's sitting
Dialogue: 0,0:08:33.31,0:08:38.27,Default,,0000,0000,0000,,right in the path of this moving\Nobject as a function of
Dialogue: 0,0:08:38.27,0:08:42.27,Default,,0000,0000,0000,,the actual period of this wave\Nsource, the wave's velocity
Dialogue: 0,0:08:42.27,0:08:44.93,Default,,0000,0000,0000,,and the velocity\Nof the source.
Dialogue: 0,0:08:44.93,0:08:46.67,Default,,0000,0000,0000,,Now, if we wanted the frequency,\Nwe just take the
Dialogue: 0,0:08:46.67,0:08:48.14,Default,,0000,0000,0000,,inverse of this.
Dialogue: 0,0:08:48.14,0:08:49.34,Default,,0000,0000,0000,,So let's do that.
Dialogue: 0,0:08:49.34,0:08:52.64,Default,,0000,0000,0000,,So the frequency of the\Nobserver-- so this is how many
Dialogue: 0,0:08:52.64,0:08:54.63,Default,,0000,0000,0000,,seconds it takes for him\Nto see the next cycle.
Dialogue: 0,0:08:54.63,0:08:57.11,Default,,0000,0000,0000,,If you want cycles per second,\Nyou take the inverse.
Dialogue: 0,0:08:57.11,0:08:58.88,Default,,0000,0000,0000,,So the frequency of the observer\Nis just going to be
Dialogue: 0,0:08:58.88,0:08:59.60,Default,,0000,0000,0000,,the inverse of this.
Dialogue: 0,0:08:59.60,0:09:02.06,Default,,0000,0000,0000,,So if we take the inverse of\Nthis whole expression, we're
Dialogue: 0,0:09:02.06,0:09:07.80,Default,,0000,0000,0000,,going to get 1 over t sub\Ns times v sub w over the
Dialogue: 0,0:09:07.80,0:09:10.84,Default,,0000,0000,0000,,velocity of the wave minus\Nthe velocity the source.
Dialogue: 0,0:09:10.84,0:09:13.74,Default,,0000,0000,0000,,And of course, 1 over the period\Nfrom the point of view
Dialogue: 0,0:09:13.74,0:09:16.58,Default,,0000,0000,0000,,of the source, this\Nis the same thing.
Dialogue: 0,0:09:16.58,0:09:18.84,Default,,0000,0000,0000,,This right here is the\Nsame thing as the
Dialogue: 0,0:09:18.84,0:09:20.26,Default,,0000,0000,0000,,frequency of the source.
Dialogue: 0,0:09:20.26,0:09:21.07,Default,,0000,0000,0000,,So there you have it.
Dialogue: 0,0:09:21.07,0:09:22.16,Default,,0000,0000,0000,,We have our two relations.
Dialogue: 0,0:09:22.16,0:09:26.01,Default,,0000,0000,0000,,At least if you are in the path,\Nif the velocity of the
Dialogue: 0,0:09:26.01,0:09:28.69,Default,,0000,0000,0000,,source is going in\Nyour direction,
Dialogue: 0,0:09:28.69,0:09:30.31,Default,,0000,0000,0000,,then we have our formulas.
Dialogue: 0,0:09:30.31,0:09:34.19,Default,,0000,0000,0000,,And I'll rewrite them, just\Nbecause the observed period of
Dialogue: 0,0:09:34.19,0:09:37.60,Default,,0000,0000,0000,,the observer is going to be the\Nperiod from the point of
Dialogue: 0,0:09:37.60,0:09:42.06,Default,,0000,0000,0000,,view of the source times the\Nvelocity of the wave minus the
Dialogue: 0,0:09:42.06,0:09:44.08,Default,,0000,0000,0000,,velocity of the source-- that's\Nthe velocity of the
Dialogue: 0,0:09:44.08,0:09:47.65,Default,,0000,0000,0000,,source-- divided by the velocity\Nof the wave itself.
Dialogue: 0,0:09:47.65,0:09:51.64,Default,,0000,0000,0000,,The frequency, from the point\Nof view of this observer, is
Dialogue: 0,0:09:51.64,0:09:53.56,Default,,0000,0000,0000,,just the inverse of that,\Nwhich is the frequency.
Dialogue: 0,0:09:53.56,0:09:56.59,Default,,0000,0000,0000,,The inverse of the period is the\Nfrequency from the point
Dialogue: 0,0:09:56.59,0:10:00.84,Default,,0000,0000,0000,,of view of the source times\Nthe velocity of the wave
Dialogue: 0,0:10:00.84,0:10:03.73,Default,,0000,0000,0000,,divided by the velocity\Nof the wave minus the
Dialogue: 0,0:10:03.73,0:10:05.45,Default,,0000,0000,0000,,velocity of the source.
Dialogue: 0,0:10:05.45,0:10:07.64,Default,,0000,0000,0000,,In the next video, I'll do the\Nexact same exercise, but I'll
Dialogue: 0,0:10:07.64,0:10:10.40,Default,,0000,0000,0000,,just think about what happens to\Nthe observer that's sitting
Dialogue: 0,0:10:10.40,0:10:11.96,Default,,0000,0000,0000,,right there.