1 00:00:00 --> 00:00:00,199 2 00:00:00,199 --> 00:00:04,142 Before we're going to dive into electromagnetic waves, 3 00:00:04,142 --> 00:00:08,606 I would like to discuss a few more mechanical resonances with 4 00:00:08,606 --> 00:00:09,797 you. Last Friday, 5 00:00:09,797 --> 00:00:14,038 we discussed the resonances of string instruments and wind 6 00:00:14,038 --> 00:00:17,163 instruments. But there are several that you 7 00:00:17,163 --> 00:00:20,883 see around you quite often -- without realizing it, 8 00:00:20,883 --> 00:00:24,975 perhaps -- that you're looking at a resonance frequency. 9 00:00:24,975 --> 00:00:30,407 You may have noticed that traffic signs have the tendency, 10 00:00:30,407 --> 00:00:33,853 sometimes, to do this, and at certain wind speeds, 11 00:00:33,853 --> 00:00:37,089 they go like this. Enormously strong amplitude, 12 00:00:37,089 --> 00:00:39,833 that's a form of resonance. Undoubtedly, 13 00:00:39,833 --> 00:00:43,772 you have been motels or at homes where you open a faucet, 14 00:00:43,772 --> 00:00:47,57 and then all of a sudden, when the water's running in a 15 00:00:47,57 --> 00:00:50,454 certain way, you hear an incredible noise, 16 00:00:50,454 --> 00:00:53,761 a terrible noise. You close the faucet a little, 17 00:00:53,761 --> 00:00:57,348 or you open it a little further, and that noise goes 18 00:00:57,348 --> 00:00:59,67 away. That's clearly an example of 19 00:00:59,67 --> 00:01:02,938 resonance. You drive your car, 20 00:01:02,938 --> 00:01:06,494 or you're in someone else's car, and at a certain speed, 21 00:01:06,494 --> 00:01:09,145 something begins to rattle. Very annoying. 22 00:01:09,145 --> 00:01:11,214 You go a little faster, it stops. 23 00:01:11,214 --> 00:01:13,283 You go a little slower, it stops. 24 00:01:13,283 --> 00:01:16,775 Or, if you go a little faster, something else begins to 25 00:01:16,775 --> 00:01:20,396 rattle, there's some other resonance of something else in 26 00:01:20,396 --> 00:01:21,818 the car. And of course, 27 00:01:21,818 --> 00:01:25,245 there are cars whereby something rattles at any speed. 28 00:01:25,245 --> 00:01:27,443 But in any case, there's this idea, 29 00:01:27,443 --> 00:01:30,159 then, of resonance, which is all around us. 30 00:01:30,159 --> 00:01:33,845 I remember when I was in a student, 31 00:01:33,845 --> 00:01:38,254 and when we had an after-dinner speaker which we didn't like 32 00:01:38,254 --> 00:01:42,738 out, we would very quickly empty our wine glasses -- in those 33 00:01:42,738 --> 00:01:47,372 days, we were still allowed to drink, by the way -- and what we 34 00:01:47,372 --> 00:01:51,482 would do is the following, something extremely annoying. 35 00:01:51,482 --> 00:01:55,443 We would generate the fundamental of our wine glasses. 36 00:01:55,443 --> 00:01:58,208 You take your finger, you make it wet, 37 00:01:58,208 --> 00:02:00,6 and you rub it like this. Listen. 38 00:02:00,6 --> 00:02:03,888 [Rubs glass]. Believe me, if hundred students 39 00:02:03,888 --> 00:02:07,245 do that, it's very annoying. 40 00:02:07,245 --> 00:02:09,829 But it's also extremely effective. 41 00:02:09,829 --> 00:02:13,588 Speaker -- speaker gets the message very quickly. 42 00:02:13,588 --> 00:02:16,486 [Rubs glass]. What the glass is doing, 43 00:02:16,486 --> 00:02:20,323 it's the fundamental of the glass, it's the lowest 44 00:02:20,323 --> 00:02:23,691 frequency, the glass is actually doing this. 45 00:02:23,691 --> 00:02:27,763 And there are rumors that people can break glasses by 46 00:02:27,763 --> 00:02:30,739 singing. And we'll talk about that in a 47 00:02:30,739 --> 00:02:32,619 minute. Um, I remember a, 48 00:02:32,619 --> 00:02:34,42 um, commercial, Memorex. 49 00:02:34,42 --> 00:02:40,312 Memorex is an audio tape. And they bragged about breaking 50 00:02:40,312 --> 00:02:44,053 glasses -- some of you may actually have seen that 51 00:02:44,053 --> 00:02:45,81 commercial. There was a, 52 00:02:45,81 --> 00:02:49,704 uh, a picture that I can show you that goes with the 53 00:02:49,704 --> 00:02:52,911 commercial, and then a very dramatic story. 54 00:02:52,911 --> 00:02:56,194 The story is that someone goes to a concert. 55 00:02:56,194 --> 00:03:00,318 And there is a woman singer, puts a glass on the table, 56 00:03:00,318 --> 00:03:03,983 raises her voice, this the resonance frequency of 57 00:03:03,983 --> 00:03:08,717 the glass, [pshew!], and there goes the glass. 58 00:03:08,717 --> 00:03:11,481 And this gentleman was recording it, 59 00:03:11,481 --> 00:03:14,954 of course, on his Memorex tape. So let's, um, 60 00:03:14,954 --> 00:03:16,849 see this, uh, this slide. 61 00:03:16,849 --> 00:03:20,244 So if we get the slide -- yes! You see this, 62 00:03:20,244 --> 00:03:23,638 um, this glass, maybe you can focus a little 63 00:03:23,638 --> 00:03:26,086 better John, thank you. Memorex. 64 00:03:26,086 --> 00:03:31,059 So the story then goes that the guy goes home and tells his wife 65 00:03:31,059 --> 00:03:34,217 about this. Well, she is smart enough not 66 00:03:34,217 --> 00:03:38,085 to believe this story. But he plays back his tape. 67 00:03:38,085 --> 00:03:43,259 And at the moment that this glass breaks at the 68 00:03:43,259 --> 00:03:47,119 concert, he has some wineglasses himself at home, 69 00:03:47,119 --> 00:03:49,853 and lo and behold, they also break. 70 00:03:49,853 --> 00:03:53,391 And so the idea is, that is the commercial -- 71 00:03:53,391 --> 00:03:57,813 that's the great pitch of Memorex -- that the reason why 72 00:03:57,813 --> 00:04:02,638 they break at home is because of the enormous quality of this 73 00:04:02,638 --> 00:04:06,095 tape which is made of very special material. 74 00:04:06,095 --> 00:04:09,794 And the material, as you could have read on the 75 00:04:09,794 --> 00:04:14,377 box, is a very special chemical compound, 76 00:04:14,377 --> 00:04:16,76 it is M R X two. Two atoms of X, 77 00:04:16,76 --> 00:04:20,603 one of R, and one of M, and then you make it oxide, 78 00:04:20,603 --> 00:04:25,061 and then you have the best tape that you can imagine in the 79 00:04:25,061 --> 00:04:27,597 world. Well, they overlook a small 80 00:04:27,597 --> 00:04:30,902 detail, and that is that, um, for one thing, 81 00:04:30,902 --> 00:04:35,36 a tape recorder would never generate enough volume to break 82 00:04:35,36 --> 00:04:39,279 a glass in the first place. But in the second place, 83 00:04:39,279 --> 00:04:43,814 the glasses that this guy had at home, obviously didn't have 84 00:04:43,814 --> 00:04:47,764 exactly the same resonance frequency as 85 00:04:47,764 --> 00:04:51,023 the glass at the concert. So this could never had 86 00:04:51,023 --> 00:04:53,671 happened. But like with all commercials, 87 00:04:53,671 --> 00:04:56,727 you know that you're being swindled, and this, 88 00:04:56,727 --> 00:05:00,394 of course, no exception. I've always questioned whether 89 00:05:00,394 --> 00:05:04,197 it is actually possible that a person, without the aid of 90 00:05:04,197 --> 00:05:07,456 strong amplification, and without the aid of huge 91 00:05:07,456 --> 00:05:11,123 sound volumes which you can generate with loudspeakers, 92 00:05:11,123 --> 00:05:13,704 whether you can actually break a glass. 93 00:05:13,704 --> 00:05:17,032 I've always wondered about that. 94 00:05:17,032 --> 00:05:20,302 People say it can be done. Caruso, famous singer, 95 00:05:20,302 --> 00:05:22,687 was known for being able to do that. 96 00:05:22,687 --> 00:05:26,365 He put the glass there, he would rub it with his finger 97 00:05:26,365 --> 00:05:29,499 so that he knew the resonance frequency [kllk], 98 00:05:29,499 --> 00:05:32,156 and there he would go, and [poit] bingo. 99 00:05:32,156 --> 00:05:34,609 Frankly speaking, I don't believe it. 100 00:05:34,609 --> 00:05:38,833 I don't believe it can be done by a human being without the aid 101 00:05:38,833 --> 00:05:42,58 of amplifiers and speakers. And when I lectured eight oh 102 00:05:42,58 --> 00:05:46,327 one, several years ago, together with 103 00:05:46,327 --> 00:05:49,97 Professor Feld here at MIT, we discussed the -- the 104 00:05:49,97 --> 00:05:54,05 possibility of designing something that actually would be 105 00:05:54,05 --> 00:05:57,912 able to break a glass. And -- and he actually deserved 106 00:05:57,912 --> 00:06:01,555 a lot of credit for that, he worked with a graduate 107 00:06:01,555 --> 00:06:05,635 student, and he managed to design a setup that works most 108 00:06:05,635 --> 00:06:08,549 of the time. But don't put your hopes too 109 00:06:08,549 --> 00:06:11,027 high, it doesn't work all the time. 110 00:06:11,027 --> 00:06:14,743 So here is a wineglass, the same series as that one. 111 00:06:14,743 --> 00:06:18,021 By the time -- when -- when he got it to work, 112 00:06:18,021 --> 00:06:21,907 we bought five hundred of those glasses 113 00:06:21,907 --> 00:06:25,408 -- we got a good discount, by the way, because we wanted 114 00:06:25,408 --> 00:06:28,335 to be sure that we can do it for years to come. 115 00:06:28,335 --> 00:06:31,708 So here's the wine glass, and here is the loudspeaker, 116 00:06:31,708 --> 00:06:34,954 and we are going to generate sound very close to the 117 00:06:34,954 --> 00:06:38,455 resonance frequency of this glass, which we have already 118 00:06:38,455 --> 00:06:42,21 determined before you came in, four hundred and eighty eight 119 00:06:42,21 --> 00:06:44,437 Hertz. You're going to see the glass 120 00:06:44,437 --> 00:06:48,129 there, and to make you see, actually, this wonderful motion 121 00:06:48,129 --> 00:06:50,929 of the glass, we will strobe it with light at 122 00:06:50,929 --> 00:06:54,299 a frequency slightly different 123 00:06:54,299 --> 00:06:58,728 from the frequency of the sound so you see the glass move very 124 00:06:58,728 --> 00:07:01,342 slowly. And then we will increase the 125 00:07:01,342 --> 00:07:04,682 volume of the speaker, and then with some like, 126 00:07:04,682 --> 00:07:08,966 if we are right on resonance, [poit], the glass may actually 127 00:07:08,966 --> 00:07:11,58 break. I think this is the sound that 128 00:07:11,58 --> 00:07:14,049 you're going to hear at low volume. 129 00:07:14,049 --> 00:07:16,591 [tone]. And I think I turned on the, 130 00:07:16,591 --> 00:07:20,584 um, the strobe light now. [tone] So I'm going to go make 131 00:07:20,584 --> 00:07:24,651 it dark. [tone] And I want to warn you 132 00:07:24,651 --> 00:07:29,284 that the sound level is going to be quite high. 133 00:07:29,284 --> 00:07:35,428 [tone] I will have to protect my ears, [tone] and you actually 134 00:07:35,428 --> 00:07:40,666 may have to do the same. [tone] I will first increase 135 00:07:40,666 --> 00:07:46,407 the volume of the sound to see whether I'm close enough to 136 00:07:46,407 --> 00:07:50,537 resonance. [tone] So this slow motion that 137 00:07:50,537 --> 00:07:55,875 you see [tone] is the result [tone] of the 138 00:07:55,875 --> 00:08:12,354 strobe, [tone] which is not exactly at the same frequency as 139 00:08:12,354 --> 00:08:22,688 the glass. I can change that a little. 140 00:08:22,688 --> 00:08:33,86 [tone] All right. So we are very close to 141 00:08:33,86 --> 00:08:44,194 resonance. [tone] The glass is clearly 142 00:08:44,194 --> 00:08:58,718 responding to the sound, [tone] and now I will [tone] 143 00:08:58,718 --> 00:09:14,358 cover my ears [tone] and slowly increase the [tone] sound 144 00:09:14,358 --> 00:09:21,899 volume. [tone] 145 00:09:21,899 --> 00:09:38,782 I can't go any louder. [tone]. 146 00:09:38,782 --> 00:09:54,5 It's tough glass. [tone] 147 00:09:54,5 --> 00:10:01,16 [glass breaking] [tone] It was a tough glass. 148 00:10:01,16 --> 00:10:07,517 [applause]. I think you will probably agree 149 00:10:07,517 --> 00:10:17,053 with me now that for a person to do that without electronic help 150 00:10:17,053 --> 00:10:26,437 is just not so believable. The most dramatic example of 151 00:10:26,437 --> 00:10:31,013 destructive resonance is the collapse of the bridge in Tacoma 152 00:10:31,013 --> 00:10:34,674 in nineteen forty. Many of you may have seen that 153 00:10:34,674 --> 00:10:37,953 dramatic movie, but some of you may not have 154 00:10:37,953 --> 00:10:40,775 seen it. And even if you have seen it, 155 00:10:40,775 --> 00:10:44,817 it's worth seeing it again. With a little bit of wind, 156 00:10:44,817 --> 00:10:49,392 there's a little bit more wind, and just like with these wind 157 00:10:49,392 --> 00:10:53,816 instruments, you're dumping a whole spectrum of frequencies 158 00:10:53,816 --> 00:11:00,666 onto a wind instrument, and it picks out the resonance 159 00:11:00,666 --> 00:11:04,091 frequency. And this bridge, 160 00:11:04,091 --> 00:11:10,678 as you're going to see, picks out its own resonance 161 00:11:10,678 --> 00:11:16,212 frequencies. And the consequences are quite 162 00:11:16,212 --> 00:11:20,032 dramatic. So if you can start, 163 00:11:20,032 --> 00:11:26,092 Marcos, with this movie. [sniffles]. 164 00:11:26,092 --> 00:11:29,156 It was nineteen forty, and at this, 165 00:11:29,156 --> 00:11:33,842 uh, in Washington State. Movie: On the First of July, 166 00:11:33,842 --> 00:11:37,987 nineteen forty, a delegation of citizens met in 167 00:11:37,987 --> 00:11:41,501 Washington State. Movie: The weather was 168 00:11:41,501 --> 00:11:46,367 beautiful, the occasion historic, and the speech-making 169 00:11:46,367 --> 00:11:49,43 and fanfare altogether appropriate. 170 00:11:49,43 --> 00:11:54,296 Movie: This was the grand opening of the Tacoma Narrows 171 00:11:54,296 --> 00:11:58,927 Bridge. Movie: From the beginning, 172 00:11:58,927 --> 00:12:03,077 the bridge, which spanned Puget Sound between Seattle and 173 00:12:03,077 --> 00:12:07,302 Tacoma, was travel in style. Movie: As well it should have 174 00:12:07,302 --> 00:12:09,822 been. The Tacoma Narrows Bridge was 175 00:12:09,822 --> 00:12:13,157 one of the longer suspension bridges on Earth. 176 00:12:13,157 --> 00:12:16,937 Movie: And, if somebody hadn't overlooked something, 177 00:12:16,937 --> 00:12:21,31 it probably would have remained one of the longer suspension 178 00:12:21,31 --> 00:12:24,868 bridges on Earth. Movie: The problem wasn't that, 179 00:12:24,868 --> 00:12:28,5 right from the beginning, alot of 180 00:12:28,5 --> 00:12:32,825 people didn't pay alot of attention to details. 181 00:12:32,825 --> 00:12:36,492 They did. Movie: But somewhere along the 182 00:12:36,492 --> 00:12:41,758 line -- and this was obvious in the end -- it looks as if 183 00:12:41,758 --> 00:12:47,305 someone forgot -- Look at those cables over [unintelligible] 184 00:12:47,305 --> 00:12:51,913 Movie: -- of resonance. Movie: Among other things, 185 00:12:51,913 --> 00:12:57,273 the Tacoma Narrows Bridge was the most spectacular Aeolian 186 00:12:57,273 --> 00:13:01,749 harp in history. Movie: Unfortunately, 187 00:13:01,749 --> 00:13:06,416 its first performance was destined to run only about four 188 00:13:06,416 --> 00:13:08,916 months. Movie: In the meantime, 189 00:13:08,916 --> 00:13:12,582 she was a beautiful bridge. Movie: Beautiful, 190 00:13:12,582 --> 00:13:16,915 but a little strange. Movie: Even before construction 191 00:13:16,915 --> 00:13:20,415 was completed, people observed its peculiar 192 00:13:20,415 --> 00:13:23,165 behavior. Movie: That was because, 193 00:13:23,165 --> 00:13:27,498 even in a light breeze, ripples ran along the bridge. 194 00:13:27,498 --> 00:13:30,831 After a while, one of the local humorists 195 00:13:30,831 --> 00:13:34,586 called her Galloping Gertie. 196 00:13:34,586 --> 00:13:39,017 Movie: And for fairly obvious reasons, the name stuck, 197 00:13:39,017 --> 00:13:43,532 at least until the seventh of November, nineteen forty. 198 00:13:43,532 --> 00:13:47,044 Movie: Then as now, Seattle and Tacoma were 199 00:13:47,044 --> 00:13:50,138 sports-minded cities. For four months, 200 00:13:50,138 --> 00:13:54,904 a regional sport was to drive across the bridge on a windy 201 00:13:54,904 --> 00:13:57,579 day. Movie: While some claimed it 202 00:13:57,579 --> 00:14:01,76 was like riding a roller coaster, others found it a 203 00:14:01,76 --> 00:14:06,096 little disconcerting to see the car in 204 00:14:06,096 --> 00:14:08,754 front disappear. [laughter] Movie: 205 00:14:08,754 --> 00:14:13,587 How popular this bridge sport was, or to what extent it might 206 00:14:13,587 --> 00:14:17,614 have spread across the country, is anybody's guess. 207 00:14:17,614 --> 00:14:20,996 Movie: On November seventh, nineteen forty, 208 00:14:20,996 --> 00:14:25,507 the winds were relatively moderate, about forty miles per 209 00:14:25,507 --> 00:14:28,084 hour. Movie: A mew mode appeared. 210 00:14:28,084 --> 00:14:31,709 Rather than ripple, the bridge began to twist. 211 00:14:31,709 --> 00:14:35,575 Movie: A wind of forty miles per 212 00:14:35,575 --> 00:14:40,296 hour is not too strong, but it was strong enough to 213 00:14:40,296 --> 00:14:43,6 start the bridge twisting violently. 214 00:14:43,6 --> 00:14:48,888 I Contacted the physics teacher of the local high school, 215 00:14:48,888 --> 00:14:54,742 and we'll see him very shortly. Thought he might be able to fix 216 00:14:54,742 --> 00:14:56,442 it. There he comes. 217 00:14:56,442 --> 00:15:00,785 I've known him some, he told me that it was his 218 00:15:00,785 --> 00:15:03,618 father. No other example of re- 219 00:15:03,618 --> 00:15:09,283 destructive resonance is more impressive than 220 00:15:09,283 --> 00:15:10,931 this one. All right. 221 00:15:10,931 --> 00:15:16,135 So now, we've had so much fun, and we have to really get into 222 00:15:16,135 --> 00:15:20,471 electromagnetic waves. So we turn back to Maxwell's 223 00:15:20,471 --> 00:15:25,848 equations as you see them here. And Maxwell -- who was credited 224 00:15:25,848 --> 00:15:30,098 for this extra term that he added to Ampere's Law, 225 00:15:30,098 --> 00:15:34,781 the displacement current term, was able to predict that 226 00:15:34,781 --> 00:15:39,204 electromagnetic waves should exist, he predicted the 227 00:15:39,204 --> 00:15:45,151 existence of radio waves, which were later discovered by 228 00:15:45,151 --> 00:15:49,279 Hertz, and that was a great victory for the theory. 229 00:15:49,279 --> 00:15:53,903 But, as I will show you today, there was another enormous 230 00:15:53,903 --> 00:15:58,362 victory around the corner. Electric and magnetic fields 231 00:15:58,362 --> 00:16:02,656 can move through space and satisfy all four Maxwell's 232 00:16:02,656 --> 00:16:06,042 equations. The electric field results from 233 00:16:06,042 --> 00:16:10,501 a changing magnetic field, and a magnetic field results 234 00:16:10,501 --> 00:16:16,779 from a changing electric field. So one exists at the mercy of 235 00:16:16,779 --> 00:16:21,286 the other, and the other exists at the mercy of one. 236 00:16:21,286 --> 00:16:26,058 Together, they propagate through space -- they can even 237 00:16:26,058 --> 00:16:30,653 propagate through vacuum, where there are no charges, 238 00:16:30,653 --> 00:16:33,392 and where there are no currents. 239 00:16:33,392 --> 00:16:37,28 Very mysterious. I will write down a possible 240 00:16:37,28 --> 00:16:42,14 solution of an electromagnetic wave which meets all four 241 00:16:42,14 --> 00:16:47,377 Maxwell's equations, and this is the graphical 242 00:16:47,377 --> 00:16:51,932 display of those waves that I'm going to write down. 243 00:16:51,932 --> 00:16:55,861 But I will discuss that with you in a minute. 244 00:16:55,861 --> 00:17:01,041 The electric field is only in the direction of X -- this is 245 00:17:01,041 --> 00:17:04,434 the magnitude, the largest value of the 246 00:17:04,434 --> 00:17:08,81 electric field -- it's only in the direction of X. 247 00:17:08,81 --> 00:17:13,007 Cosine K Z minus omega T. This is the frequency, 248 00:17:13,007 --> 00:17:17,74 and the minus sign tells you that it is 249 00:17:17,74 --> 00:17:21,077 traveling in the plus Z direction. 250 00:17:21,077 --> 00:17:25,424 B, the associated magnetic field, is B zero, 251 00:17:25,424 --> 00:17:30,682 only in the Y direction, with exactly the same cosine 252 00:17:30,682 --> 00:17:35,332 minus omega T term. So if I plot this at time T 253 00:17:35,332 --> 00:17:40,084 equals zero, then you see this curve right here. 254 00:17:40,084 --> 00:17:44,23 And you see the magnetic field curve here. 255 00:17:44,23 --> 00:17:49,083 The magnetic field is only in the Y 256 00:17:49,083 --> 00:17:53,547 direction, and the electric field is only in the X 257 00:17:53,547 --> 00:17:56,918 direction. And this is a package that, 258 00:17:56,918 --> 00:18:01,565 together, moves in the direction of plus Z with this 259 00:18:01,565 --> 00:18:04,663 speed, which is omega divided by K. 260 00:18:04,663 --> 00:18:10,221 And the wavelength from here to here is N two pi divided by K. 261 00:18:10,221 --> 00:18:15,232 We call then plane waves, and the reason why we cal them 262 00:18:15,232 --> 00:18:18,877 plane waves is that, if you take a plane, 263 00:18:18,877 --> 00:18:25,293 anywhere perpendicular to Z, that no matter where you are in 264 00:18:25,293 --> 00:18:30,21 that plane, at that moment in time, the E and the B vector are 265 00:18:30,21 --> 00:18:32,87 everywhere in that plane the same. 266 00:18:32,87 --> 00:18:37,303 So think of this as a plane perpendicular to the Z axis, 267 00:18:37,303 --> 00:18:40,447 and then this whole train passes by you. 268 00:18:40,447 --> 00:18:44,477 And so you see the electric field vector like this, 269 00:18:44,477 --> 00:18:47,46 becomes zero, like this, becomes zero, 270 00:18:47,46 --> 00:18:50,684 like this. And the magnetic field vector, 271 00:18:50,684 --> 00:18:54,392 maximum, zero, this direction, 272 00:18:54,392 --> 00:18:58,236 and so on. But that's why they're called 273 00:18:58,236 --> 00:19:02,18 plane waves. These equations only satisfy 274 00:19:02,18 --> 00:19:06,123 Maxwell's equations under two conditions. 275 00:19:06,123 --> 00:19:11,545 And one condition is that B zero is E zero divided by C, 276 00:19:11,545 --> 00:19:16,475 and the other condition is that omega divided by K, 277 00:19:16,475 --> 00:19:21,108 which is the velocity, with which it propagates, 278 00:19:21,108 --> 00:19:25,545 I will call that C -- in vacuum, 279 00:19:25,545 --> 00:19:30,199 we call the velocity of electromagnetic radiation C -- 280 00:19:30,199 --> 00:19:34,942 that is one divided by the square root of epsilon zero, 281 00:19:34,942 --> 00:19:37,314 mu zero. If that's the case, 282 00:19:37,314 --> 00:19:41,617 my two equations will satisfy Maxwell's equations. 283 00:19:41,617 --> 00:19:44,34 Imagine the victory for Maxwell. 284 00:19:44,34 --> 00:19:48,907 Maxwell was not only able to predict the existence of 285 00:19:48,907 --> 00:19:53,562 electromagnetic waves, but he was even able to predict 286 00:19:53,562 --> 00:19:57,554 that they would move through vacuum 287 00:19:57,554 --> 00:20:01,04 with that speed. What an unbelievable victory, 288 00:20:01,04 --> 00:20:05,146 when you come to think of it, that epsilon zero can be 289 00:20:05,146 --> 00:20:09,639 measured -- in a static way, if follows from Coulomb's law, 290 00:20:09,639 --> 00:20:14,287 has nothing to do with the B dT, has nothing to do with the E 291 00:20:14,287 --> 00:20:16,223 dT. Has nothing to do with 292 00:20:16,223 --> 00:20:19,554 traveling waves. Epsilon zero is about eight 293 00:20:19,554 --> 00:20:24,047 point eight five times ten to the minus twelve in SI units. 294 00:20:24,047 --> 00:20:29,89 Mu zero is equally static, can be measured from the force 295 00:20:29,89 --> 00:20:33,516 at which two wires, through which you run a 296 00:20:33,516 --> 00:20:37,573 current, attract each other. No dB dT, no dE dT, 297 00:20:37,573 --> 00:20:41,717 there's nothing to do with electromagnetic waves. 298 00:20:41,717 --> 00:20:46,896 Mu zero is about one point two six times ten to the minus six 299 00:20:46,896 --> 00:20:50,09 in SI units. And if you multiply them, 300 00:20:50,09 --> 00:20:55,011 and substitute them in this equation, you will find that C 301 00:20:55,011 --> 00:20:59,932 equals two point nine nine times ten to the 302 00:20:59,932 --> 00:21:03,415 eight meters per second. Unbelievable. 303 00:21:03,415 --> 00:21:08,97 What a success for that theory. It always baffles me how two 304 00:21:08,97 --> 00:21:13,584 quantities so static, an seemingly so unrelated to 305 00:21:13,584 --> 00:21:17,727 moving waves, with dB dTs and dE dTs all over 306 00:21:17,727 --> 00:21:22,435 the place, how they can predict the speed of light. 307 00:21:22,435 --> 00:21:27,802 Suppose I ask you to measure the pressure in your tires of 308 00:21:27,802 --> 00:21:32,509 your car, and I would ask you to also 309 00:21:32,509 --> 00:21:37,978 measure the voltage of your battery, and then to predict the 310 00:21:37,978 --> 00:21:41,964 speed of the car. It's almost something like 311 00:21:41,964 --> 00:21:43,725 that. It is bizarre. 312 00:21:43,725 --> 00:21:47,433 But it works, and it was a great victory, 313 00:21:47,433 --> 00:21:51,511 and of course, it justified entirely this one 314 00:21:51,511 --> 00:21:55,682 term, which is this displacement current term. 315 00:21:55,682 --> 00:21:59,668 Together, you and I will prove that this is, 316 00:21:59,668 --> 00:22:04,025 indeed, a necessary condition so 317 00:22:04,025 --> 00:22:08,019 that these equations satisfy Maxwell's equations. 318 00:22:08,019 --> 00:22:11,68 We will do it together. I will do 50 percent, 319 00:22:11,68 --> 00:22:16,34 and you will do the other 50 percent at assignment number 320 00:22:16,34 --> 00:22:18,504 nine. So we split this bill 321 00:22:18,504 --> 00:22:21,666 fifty-fifty. I will make a new drawing, 322 00:22:21,666 --> 00:22:26,409 and I will do something that I rarely ever do in lectures, 323 00:22:26,409 --> 00:22:30,237 I will give you eight minutes of hardcore math. 324 00:22:30,237 --> 00:22:37,15 You're going to hate it. I'm going to make a new 325 00:22:37,15 --> 00:22:44,067 drawing, which is not too different from what you have 326 00:22:44,067 --> 00:22:46,546 there. So this is Z, 327 00:22:46,546 --> 00:22:52,549 this is X, and this is Y. And at T equals zero, 328 00:22:52,549 --> 00:22:58,944 I'm going to draw here the electric field like so. 329 00:22:58,944 --> 00:23:04,164 So this is E zero, electric field is this 330 00:23:04,164 --> 00:23:09,45 strength, and now I'm going to apply 331 00:23:09,45 --> 00:23:15,226 Ampere's Law -- that's my half of the bargain -- closed-loop 332 00:23:15,226 --> 00:23:21,099 integral of B dot D L -- you see there -- equals epsilon zero 333 00:23:21,099 --> 00:23:26,875 times mu zero times D phi E D T. We're dealing with vacuums, 334 00:23:26,875 --> 00:23:31,379 so kappa is one, and the dielectric constant is 335 00:23:31,379 --> 00:23:34,805 one. And there is no such thing as a 336 00:23:34,805 --> 00:23:39,995 current I, because we are in empty space, 337 00:23:39,995 --> 00:23:43,399 so this whole term does not exist. 338 00:23:43,399 --> 00:23:48,763 What does Ampere's Law require? I need a closed loop, 339 00:23:48,763 --> 00:23:54,642 and I need a surface that I attach an open surface to that 340 00:23:54,642 --> 00:23:58,768 closed loop. I'm going to choose a closed 341 00:23:58,768 --> 00:24:03,719 loop in the plane Y Z. And this is going to be my 342 00:24:03,719 --> 00:24:07,742 closed loop. This here is going to be my 343 00:24:07,742 --> 00:24:12,28 closed loop. This length is L, 344 00:24:12,28 --> 00:24:16,256 and the length -- or the width, of this side, 345 00:24:16,256 --> 00:24:20,954 is lambda divided by four. I have to do a closed loop 346 00:24:20,954 --> 00:24:24,749 integral of B dot D L, I will do that last. 347 00:24:24,749 --> 00:24:29,267 I will first do the hardest part, which is the time 348 00:24:29,267 --> 00:24:33,965 derivative of the electric flux through this surface. 349 00:24:33,965 --> 00:24:38,844 The problem is that the electric field is not constant. 350 00:24:38,844 --> 00:24:45,078 The electric field is zero here, and has a maximum here, 351 00:24:45,078 --> 00:24:50,037 and falls off in this way. So I have to do an integral. 352 00:24:50,037 --> 00:24:55,454 So I'm going to make a slice here, and this slice here has a 353 00:24:55,454 --> 00:24:59,127 width D Z. And in that very narrow slice, 354 00:24:59,127 --> 00:25:03,167 the electric field is approximately constant. 355 00:25:03,167 --> 00:25:07,299 Right here, the electric field ahs this value. 356 00:25:07,299 --> 00:25:11,982 But everywhere in that slice, it has the same value, 357 00:25:11,982 --> 00:25:16,481 because remember, it's a plane wave. 358 00:25:16,481 --> 00:25:23,028 And so I will draw here a line parallel, and so everywhere in 359 00:25:23,028 --> 00:25:28,81 that slice, the electric field has exactly this value. 360 00:25:28,81 --> 00:25:33,175 And that value is given by this equation. 361 00:25:33,175 --> 00:25:38,194 If you tell me what Z is at time T equals zero, 362 00:25:38,194 --> 00:25:42,994 I know what that value is, that's this value. 363 00:25:42,994 --> 00:25:48,61 So now I have to calculate the electric flux. 364 00:25:48,61 --> 00:25:53,509 So phi of E -- I have to take the dot product between D A and 365 00:25:53,509 --> 00:25:56,938 the electric field. Remember, flux is a dot 366 00:25:56,938 --> 00:26:00,367 product, E times D A. I will choose D A up, 367 00:26:00,367 --> 00:26:04,367 because E is also up, so that makes life easy -- I 368 00:26:04,367 --> 00:26:09,184 have to remember that later, then, when I do the closed loop 369 00:26:09,184 --> 00:26:12,94 integral of B dot D L, then looking from below, 370 00:26:12,94 --> 00:26:16,614 I have to go clockwise, because I remember the 371 00:26:16,614 --> 00:26:20,264 right-hand corkscrew rule. 372 00:26:20,264 --> 00:26:25,659 So I get all my minus signs and plus signs just right. 373 00:26:25,659 --> 00:26:29,426 So D A an E are in the same direction. 374 00:26:29,426 --> 00:26:32,989 So what is D A of this little slice? 375 00:26:32,989 --> 00:26:37,162 That is L times D Z. So I get L times D Z. 376 00:26:37,162 --> 00:26:41,845 What is the local electric field in this slice? 377 00:26:41,845 --> 00:26:47,139 Well, that's that equation. So I get E zero times the 378 00:26:47,139 --> 00:26:52,507 cosine of K Z minus omega T. This X roof, 379 00:26:52,507 --> 00:26:56,968 of course, is gone, because the A and E are in the 380 00:26:56,968 --> 00:27:01,065 same direction, I have already taken that into 381 00:27:01,065 --> 00:27:04,342 account. But I have to integrate this 382 00:27:04,342 --> 00:27:08,257 now, from Z equals zero to lambda over four, 383 00:27:08,257 --> 00:27:13,173 because I have to integrate it over this whole surface. 384 00:27:13,173 --> 00:27:18,362 So that's the -- the answer. But I'm not interested in phi 385 00:27:18,362 --> 00:27:21,184 E. I have to know the phi E D T. 386 00:27:21,184 --> 00:27:24,188 So it's going to be worse for you. 387 00:27:24,188 --> 00:27:28,371 I told you, eight minutes, 388 00:27:28,371 --> 00:27:33,437 pain in the neck. So I'm going to take the time 389 00:27:33,437 --> 00:27:38,173 derivative of that function, so D phi E D T. 390 00:27:38,173 --> 00:27:43,019 L and E zero can come out, that's no problem, 391 00:27:43,019 --> 00:27:48,196 they are constants. I tae the time derivative of 392 00:27:48,196 --> 00:27:53,814 cosine K Z minus omega T, then minus omega pops out, 393 00:27:53,814 --> 00:27:57,669 and the cosine becomes a minus sign. 394 00:27:57,669 --> 00:28:05,002 So I get minus the sine of K Z minus omega T. 395 00:28:05,002 --> 00:28:11,518 And I have to do an integral -- here is my D Z, 396 00:28:11,518 --> 00:28:19,026 zero to lambda over four. This minus sign eats up this 397 00:28:19,026 --> 00:28:24,267 minus sign. I have to do the integral, 398 00:28:24,267 --> 00:28:33,192 but I do that at T equals zero. In other words, 399 00:28:33,192 --> 00:28:38,962 this thing goes away, because T equals zero. 400 00:28:38,962 --> 00:28:45,807 So I'm getting close. So I'm going to continue here, 401 00:28:45,807 --> 00:28:51,175 so I get L times E zero, I have an omega, 402 00:28:51,175 --> 00:28:57,751 and now I have to do the integral of sine K Z D Z. 403 00:28:57,751 --> 00:29:07,682 Well, the K Z means I have to get a K out, which is here, 404 00:29:07,682 --> 00:29:13,527 and then the integral of sine D Z is simply minus the cosine of 405 00:29:13,527 --> 00:29:19,183 K Z, and I have to evaluate that between zero and lambda over 406 00:29:19,183 --> 00:29:21,917 four. If I evaluate cosine K Z 407 00:29:21,917 --> 00:29:26,726 between zero and lambda over four, that's minus one. 408 00:29:26,726 --> 00:29:32,382 I'm sure you can do that alone. Times this minus one makes it 409 00:29:32,382 --> 00:29:37,191 plus one. And so the answer is L times E 410 00:29:37,191 --> 00:29:41,948 zero times omega divided by K, but we call that C, 411 00:29:41,948 --> 00:29:47,481 in vacuum, that is the speed of electromagnetic radiation. 412 00:29:47,481 --> 00:29:51,171 So this is the answer to the phi E D T. 413 00:29:51,171 --> 00:29:56,607 Now, we have to do the closed loop integral of B dot D L. 414 00:29:56,607 --> 00:30:00,491 And that is easy. At this moment in time, 415 00:30:00,491 --> 00:30:04,18 B is the maximum here, which is B zero, 416 00:30:04,18 --> 00:30:08,687 and then it falls off to zero here. 417 00:30:08,687 --> 00:30:12,81 You can see the same there. Suppose I start here, 418 00:30:12,81 --> 00:30:15,989 and I go this way, this way, this way, 419 00:30:15,989 --> 00:30:18,909 and this way. Closed loop integral. 420 00:30:18,909 --> 00:30:23,376 If I go from here to here, my B and D L are at ninety 421 00:30:23,376 --> 00:30:26,211 degree angles. B is coming to you, 422 00:30:26,211 --> 00:30:30,935 and B L i- D L is like this. So there is no contribution 423 00:30:30,935 --> 00:30:33,77 here. If you go from here to here, 424 00:30:33,77 --> 00:30:38,752 well, B is zero everywhere along the line. 425 00:30:38,752 --> 00:30:42,547 So integral B dot D L from here to here is zero. 426 00:30:42,547 --> 00:30:44,727 It's a plane wave, remember? 427 00:30:44,727 --> 00:30:47,552 B is zero here, it's also zero here, 428 00:30:47,552 --> 00:30:50,781 it's also zero here, it's also zero here. 429 00:30:50,781 --> 00:30:54,172 If you go from here to here, B and D L are, 430 00:30:54,172 --> 00:30:58,935 again, at ninety-degree angles, so there is no contribution, 431 00:30:58,935 --> 00:31:02,972 so there's only a contribution due to this portion. 432 00:31:02,972 --> 00:31:05,878 And that I B zero times the length L. 433 00:31:05,878 --> 00:31:11,691 And now you see why I chose the width lambda over four, 434 00:31:11,691 --> 00:31:15,52 so I get a very easy result. So I find, then, 435 00:31:15,52 --> 00:31:19,436 that B zero times L, which is the left part of 436 00:31:19,436 --> 00:31:23,7 Ampere's Law -- well, it's too much to give Ampere 437 00:31:23,7 --> 00:31:28,574 credit -- all the credit, because it's really Maxwell who 438 00:31:28,574 --> 00:31:31,185 added that term, the phi E D T. 439 00:31:31,185 --> 00:31:34,753 And so this, now, is epsilon zero mu zero, 440 00:31:34,753 --> 00:31:39,8 which you see upstairs there, times the result that we have 441 00:31:39,8 --> 00:31:42,933 here. Oh, by the way, 442 00:31:42,933 --> 00:31:46,06 this is E zero. Times L, times E zero, 443 00:31:46,06 --> 00:31:48,089 times C. And I lose my L. 444 00:31:48,089 --> 00:31:52,314 And you see here a result that is quite remarkable, 445 00:31:52,314 --> 00:31:56,37 even though it doesn't look so remarkable to you, 446 00:31:56,37 --> 00:31:57,892 yet. The reason is, 447 00:31:57,892 --> 00:32:01,187 that you are going to do the other half. 448 00:32:01,187 --> 00:32:04,821 You are going to apply Faraday's Law for me. 449 00:32:04,821 --> 00:32:08,709 I only used Ampere's Law, you're going to -- in 450 00:32:08,709 --> 00:32:11,92 assignment nine, use this relationship, 451 00:32:11,92 --> 00:32:16,483 which will allow you to prove this. 452 00:32:16,483 --> 00:32:22,264 And once you have this, substitute for B zero, 453 00:32:22,264 --> 00:32:28,429 E zero divided by C, and you see immediately that 454 00:32:28,429 --> 00:32:33,567 the speed of light, then, has to be this. 455 00:32:33,567 --> 00:32:37,806 This is your task. I did this end. 456 00:32:37,806 --> 00:32:44,485 Yours is not easier than mine, and I advise you also, 457 00:32:44,485 --> 00:32:50,266 use this quarter-wavelength trick. 458 00:32:50,266 --> 00:32:54,993 All right, so you can demonstrate that this is a 459 00:32:54,993 --> 00:33:00,323 necessary condition for Maxwell's equations to satisfy 460 00:33:00,323 --> 00:33:05,653 the, um -- this is not what I want -- to -- that these 461 00:33:05,653 --> 00:33:11,185 equations actually satisfy all four Maxwell's equations. 462 00:33:11,185 --> 00:33:16,817 Traveling electromagnetic waves always have the following 463 00:33:16,817 --> 00:33:21,041 properties. This is on the Web, 464 00:33:21,041 --> 00:33:24,667 so you can download that. E is perpendicular to V. 465 00:33:24,667 --> 00:33:26,961 Notice that that's what I chose. 466 00:33:26,961 --> 00:33:30,512 E is perpendicular to V. V is in the Z direction, 467 00:33:30,512 --> 00:33:34,211 and E is like this, so that's obviously why I chose 468 00:33:34,211 --> 00:33:36,727 that. B is also perpendicular to V. 469 00:33:36,727 --> 00:33:40,648 B is in the Y direction here. Only in the Y direction. 470 00:33:40,648 --> 00:33:44,866 It's also perpendicular to V, which is in the Z direction. 471 00:33:44,866 --> 00:33:48,343 E is also perpendicular to B. That's what I did. 472 00:33:48,343 --> 00:33:52,782 E in the X direction, B in the Y direction. 473 00:33:52,782 --> 00:33:55,657 E and B are in phase. That is like saying, 474 00:33:55,657 --> 00:33:59,512 if this is cosine K Z minus omega T, this also has to be 475 00:33:59,512 --> 00:34:03,368 cosine K Z minus omega T. They simultaneously go through 476 00:34:03,368 --> 00:34:06,522 zero, and they simultaneously reach a maximum. 477 00:34:06,522 --> 00:34:10,027 What is also a necessary condition, that E cross B, 478 00:34:10,027 --> 00:34:12,901 the unit vector, is in the direction of V. 479 00:34:12,901 --> 00:34:15,916 Ha, look at that, that's exactly what I did. 480 00:34:15,916 --> 00:34:19,631 If you take E and you cross it with B, you go into the 481 00:34:19,631 --> 00:34:22,295 direction Z. In fact, whenever you make 482 00:34:22,295 --> 00:34:26,025 drawings like this, you should always 483 00:34:26,025 --> 00:34:28,977 what we call a right-handed coordinate system, 484 00:34:28,977 --> 00:34:32,717 which is that X roof crossed with Y roof is always Z roof. 485 00:34:32,717 --> 00:34:35,867 If you don't do that, you got yourself into muddy 486 00:34:35,867 --> 00:34:38,097 water. And then, in case you are in 487 00:34:38,097 --> 00:34:42,1 vacuum, there is a correlation between -- a relation between B 488 00:34:42,1 --> 00:34:45,84 zero and E zero that you are going to prove with Faraday's 489 00:34:45,84 --> 00:34:48,399 Law, and then, combined with my results, 490 00:34:48,399 --> 00:34:52,27 the speed of electromagnetic radiation in vacuum is one over 491 00:34:52,27 --> 00:34:56,076 the square root of epsilon zero mu zero. 492 00:34:56,076 --> 00:35:00,646 If you know the frequency of the electromagnetic radiation, 493 00:35:00,646 --> 00:35:05,296 then the wavelength follows immediately, and so you see here 494 00:35:05,296 --> 00:35:08,685 a few examples that I've calculated for you. 495 00:35:08,685 --> 00:35:13,019 If you start out with a low frequency of thousand Hertz, 496 00:35:13,019 --> 00:35:16,802 you get a wavelength of three hundred kilometers, 497 00:35:16,802 --> 00:35:19,876 radio waves, megaHertz, still talk about 498 00:35:19,876 --> 00:35:23,343 radio waves, but when you go up in frequency, 499 00:35:23,343 --> 00:35:26,653 the wavelengths, of course, get shorter and 500 00:35:26,653 --> 00:35:30,446 shorter, we would call these radar 501 00:35:30,446 --> 00:35:33,436 waves, microwaves. If you go to ten to the 502 00:35:33,436 --> 00:35:37,666 fourteen, ten to the fifteen Hertz, you get into the domain 503 00:35:37,666 --> 00:35:41,312 of infrared and visible light, and the ultraviolet, 504 00:35:41,312 --> 00:35:45,468 and if you go even higher, then you end up with X-ray and, 505 00:35:45,468 --> 00:35:49,406 ultimately, gamma rays. All of these are members of the 506 00:35:49,406 --> 00:35:52,687 electromagnetic family, electromagnetic waves. 507 00:35:52,687 --> 00:35:56,479 This A with a little zero there stands for angstroms. 508 00:35:56,479 --> 00:36:00,489 That means ten to the minus ten meters. 509 00:36:00,489 --> 00:36:03,703 So, a whole family of electromagnetic waves, 510 00:36:03,703 --> 00:36:08,186 and we give them names so we can talk about them without ever 511 00:36:08,186 --> 00:36:11,847 mentioning the specific frequency or the -- or the 512 00:36:11,847 --> 00:36:14,313 wavelength. So given the fact that 513 00:36:14,313 --> 00:36:18,124 electromagnetic waves then travel with three hundred 514 00:36:18,124 --> 00:36:22,159 thousand kilometers per second, one foot would take one 515 00:36:22,159 --> 00:36:24,699 nanosecond. Twenty six one hundred, 516 00:36:24,699 --> 00:36:27,464 thirty meters deep. The light, for me, 517 00:36:27,464 --> 00:36:31,947 to Professor Bertozzi all the way at the end would take about 518 00:36:31,947 --> 00:36:35,336 oh point one microseconds. 519 00:36:35,336 --> 00:36:38,723 One second, light, radio waves to the moon. 520 00:36:38,723 --> 00:36:43,321 Eight minutes it takes the light from the sun to reach us. 521 00:36:43,321 --> 00:36:47,596 The light from the nearest stars will take five years. 522 00:36:47,596 --> 00:36:52,678 And the nearest large galaxy to the Earth would take two million 523 00:36:52,678 --> 00:36:55,259 years for that light to reach us. 524 00:36:55,259 --> 00:36:59,695 So when you look at that galaxy, then you see the galaxy 525 00:36:59,695 --> 00:37:02,599 the way it was two million years ago. 526 00:37:02,599 --> 00:37:06,552 In astronomy, we use as our meter 527 00:37:06,552 --> 00:37:10,139 stick, a light-year, which is the distance that 528 00:37:10,139 --> 00:37:14,116 light travels in one year, which is about ten to the 529 00:37:14,116 --> 00:37:17,625 sixteen meters. If you study a galaxy which is 530 00:37:17,625 --> 00:37:22,148 at a distance of ten billion light-years, you're looking at 531 00:37:22,148 --> 00:37:25,97 the universe the way it was ten billion years ago. 532 00:37:25,97 --> 00:37:29,245 So in astronomy, you can look back minutes, 533 00:37:29,245 --> 00:37:33,378 you can look back years, you can look back millions of 534 00:37:33,378 --> 00:37:37,746 years, but you can also look back in time 535 00:37:37,746 --> 00:37:41,526 billions of years. Most forms of electromagnetic 536 00:37:41,526 --> 00:37:45,146 radiation -- certainly light, and radio waves, 537 00:37:45,146 --> 00:37:48,123 and radar -- can reflect off surfaces. 538 00:37:48,123 --> 00:37:52,225 At least, to some degree, it depends on the surface. 539 00:37:52,225 --> 00:37:56,65 And this is the basis behind the distance determination. 540 00:37:56,65 --> 00:38:01,557 When you send a radar pulse to an airplane, or to a rainstorm, 541 00:38:01,557 --> 00:38:06,142 some of that radiation comes back at you, and you know the 542 00:38:06,142 --> 00:38:10,863 speed, and so that allowed you to calculate the 543 00:38:10,863 --> 00:38:13,815 distance. If the distance to the plane is 544 00:38:13,815 --> 00:38:18,243 D, and you send a brief pulse, and it comes back -- they call 545 00:38:18,243 --> 00:38:22,598 it the echo -- and it takes a certain amount of time to come 546 00:38:22,598 --> 00:38:26,804 back, which you can measure, then that signal has traveled 547 00:38:26,804 --> 00:38:30,347 twice the distance, so that is the speed of light 548 00:38:30,347 --> 00:38:34,332 times T, this is what you measure, the distance in time 549 00:38:34,332 --> 00:38:38,17 from the moment you sent the signal until you get the 550 00:38:38,17 --> 00:38:42,928 reflection back, and so you can calculate the 551 00:38:42,928 --> 00:38:46,353 distance. The distance to the moon can be 552 00:38:46,353 --> 00:38:49,691 measured this way. There are five corner 553 00:38:49,691 --> 00:38:54,057 reflectors on the moon. Three were left there by the 554 00:38:54,057 --> 00:38:59,364 Americans and two were left by the Soviets, in the days that it 555 00:38:59,364 --> 00:39:04,329 was still the Soviet Union. An optical telescope from Earth 556 00:39:04,329 --> 00:39:07,753 can send a very brief pulse, laser pulse, 557 00:39:07,753 --> 00:39:12,719 to these corner reflectors. The l- the time, 558 00:39:12,719 --> 00:39:16,971 the length in time of this pulse is only one-quarter of a 559 00:39:16,971 --> 00:39:18,793 nanosecond. Just imagine, 560 00:39:18,793 --> 00:39:22,97 light only travels seven centimeters in one-quarter of a 561 00:39:22,97 --> 00:39:25,931 nanosecond. So the kind of wave that you 562 00:39:25,931 --> 00:39:30,715 get is really not very much of a plane wave, the way we envision 563 00:39:30,715 --> 00:39:32,158 it. But in any case, 564 00:39:32,158 --> 00:39:36,638 this pulse goes to the moon, and then some of it comes back, 565 00:39:36,638 --> 00:39:40,967 it's reflected off these radar -- these corner reflectors, 566 00:39:40,967 --> 00:39:44,916 not radar, it's light. Laser light. 567 00:39:44,916 --> 00:39:48,761 There are two times ten to the seventeen photons, 568 00:39:48,761 --> 00:39:53,167 roughly, in one of these pulses, and only one comes back 569 00:39:53,167 --> 00:39:56,211 per ten pulses. So not much comes back. 570 00:39:56,211 --> 00:39:59,816 But it's enough, if you integrate it to get an 571 00:39:59,816 --> 00:40:04,302 accurate distance determination between us and the corner 572 00:40:04,302 --> 00:40:08,227 reflectors, the accuracy is about ten centimeters. 573 00:40:08,227 --> 00:40:13,114 And the goal is really to get a handle on the precise orbit of 574 00:40:13,114 --> 00:40:16,719 the moon. I can show you these 575 00:40:16,719 --> 00:40:22,145 corner reflectors the way they were built on Earth, 576 00:40:22,145 --> 00:40:28,222 and then I will also show an optical observatory as it is 577 00:40:28,222 --> 00:40:32,888 sending out these quarter-nanosecond pulses, 578 00:40:32,888 --> 00:40:35,493 laser light, to the moon. 579 00:40:35,493 --> 00:40:39,182 So this is, uh, one of those corner 580 00:40:39,182 --> 00:40:43,74 reflectors. They are designed in such a way 581 00:40:43,74 --> 00:40:50,801 that if light strikes it in a certain direction, 582 00:40:50,801 --> 00:40:55,794 that it reflects the light in exactly the same direction 583 00:40:55,794 --> 00:41:00,606 backwards, hundred eighty degrees, very clever design. 584 00:41:00,606 --> 00:41:04,692 And so the next slide will show you, in Texas, 585 00:41:04,692 --> 00:41:08,051 McDonald Observatory is sending, here, 586 00:41:08,051 --> 00:41:10,321 these short, brief pulses, 587 00:41:10,321 --> 00:41:12,5 laser light, to the moon, 588 00:41:12,5 --> 00:41:18,22 and what you see here is simply some scattered light of the dust 589 00:41:18,22 --> 00:41:21,464 in the Earth atmosphere. 590 00:41:21,464 --> 00:41:25,644 And then only a teeny weeny little bit of that comes back, 591 00:41:25,644 --> 00:41:29,311 but that is enough to get the distance to the moon. 592 00:41:29,311 --> 00:41:33,711 There are, on the moon -- this is enough for this slide to -- 593 00:41:33,711 --> 00:41:35,911 John -- there are, on the moon, 594 00:41:35,911 --> 00:41:38,918 several cameras. They were left there by a 595 00:41:38,918 --> 00:41:41,264 surveyor, they are small cameras. 596 00:41:41,264 --> 00:41:44,491 The lens, I think, is only two inches across. 597 00:41:44,491 --> 00:41:47,864 And they keep an eye on the Earth all the time. 598 00:41:47,864 --> 00:41:52,485 Something that you may never have thought of, 599 00:41:52,485 --> 00:41:55,795 if you were on the moon, and you look at the Earth, 600 00:41:55,795 --> 00:41:59,105 and the Earth is there, say, that an hour from now, 601 00:41:59,105 --> 00:42:02,615 the Earth will still be there. And ten hours from now, 602 00:42:02,615 --> 00:42:06,124 the Earth will still be there, and ten years from now, 603 00:42:06,124 --> 00:42:09,567 the Earth will still be there. As seen from the moon, 604 00:42:09,567 --> 00:42:13,076 the Earth never moves. Of course, it rotates about its 605 00:42:13,076 --> 00:42:14,599 axis. You will see that. 606 00:42:14,599 --> 00:42:18,637 You will also see that certain parts of the Earth are at night 607 00:42:18,637 --> 00:42:21,22 and others are at day, that's different, 608 00:42:21,22 --> 00:42:24,994 but it's always in the same direction. 609 00:42:24,994 --> 00:42:29,3 So it's very easy for these cameras to keep an eye on us, 610 00:42:29,3 --> 00:42:32,529 so to speak. All you have to do is aim them 611 00:42:32,529 --> 00:42:35,989 in one direction, and you never have to change 612 00:42:35,989 --> 00:42:39,527 that direction. Imagine that you and I were now 613 00:42:39,527 --> 00:42:42,987 on the moon, and we were looking at the Earth. 614 00:42:42,987 --> 00:42:46,985 And you, for instance, would see the Earth as you see 615 00:42:46,985 --> 00:42:49,292 it here. Here is North America, 616 00:42:49,292 --> 00:42:53,06 and this part of the Earth happens to be daylight, 617 00:42:53,06 --> 00:42:56,674 and here it's night. And this is the moment that 618 00:42:56,674 --> 00:43:00,45 these cameras are going to take a 619 00:43:00,45 --> 00:43:04,025 picture of the Earth. So you expect to see a lot of 620 00:43:04,025 --> 00:43:08,387 light here, and you expect this to be night, here is New York. 621 00:43:08,387 --> 00:43:12,748 You may think that there is so much light coming from New York 622 00:43:12,748 --> 00:43:16,896 that you may actually see New York, that a picture taken by 623 00:43:16,896 --> 00:43:20,042 these cameras actually may show you New York. 624 00:43:20,042 --> 00:43:23,045 Well, you won't, but you see something else 625 00:43:23,045 --> 00:43:26,763 which is very dramatic, that's why I show this to you 626 00:43:26,763 --> 00:43:31,823 -- because the picture you're going to see next -- John, 627 00:43:31,823 --> 00:43:35,932 you can show it -- is at the time that two observatories on 628 00:43:35,932 --> 00:43:39,758 Earth were both sending these laser pulses to the moon. 629 00:43:39,758 --> 00:43:43,655 And here you see one in Arizona, and here you see one in 630 00:43:43,655 --> 00:43:46,348 California. But you don't see New York. 631 00:43:46,348 --> 00:43:49,394 Isn't that amazing? That you're on the moon, 632 00:43:49,394 --> 00:43:52,299 and you know there's really life on Earth, 633 00:43:52,299 --> 00:43:55,842 someone is blinking at you. Well, you don't see the 634 00:43:55,842 --> 00:43:58,251 blinking, but you see these lights. 635 00:43:58,251 --> 00:44:01,159 Very dramatic shot. 636 00:44:01,159 --> 00:44:05,282 Thanks, uh, John, that's fine. 637 00:44:05,282 --> 00:44:12,535 Radio waves can be generated by oscillating charges. 638 00:44:12,535 --> 00:44:19,929 I will talk about that a great deal the next lecture. 639 00:44:19,929 --> 00:44:30,025 So you run alternating current through wires called antennas -- 640 00:44:30,025 --> 00:44:35,523 this is an antenna -- and then you create electromagnetic 641 00:44:35,523 --> 00:44:39,057 waves. And radio stations transmit at 642 00:44:39,057 --> 00:44:42,787 a well-defined frequency. For instance, 643 00:44:42,787 --> 00:44:47,793 WEEI transmits at eight hundred and fifty kiloHertz, 644 00:44:47,793 --> 00:44:52,407 wavelength three hundred and fifty three meters. 645 00:44:52,407 --> 00:44:57,61 Eight hundred and fifty kiloHertz is an extremely high 646 00:44:57,61 --> 00:45:02,617 frequency. How come I can hear things, 647 00:45:02,617 --> 00:45:06,916 that I can hear music, and that k- I hear someone 648 00:45:06,916 --> 00:45:09,962 speak? Well, this signal -- we call 649 00:45:09,962 --> 00:45:13,813 this the carrier wave -- is being modulated. 650 00:45:13,813 --> 00:45:19,278 The strength of that signal is modulated with the frequency of 651 00:45:19,278 --> 00:45:21,696 audible sound, we call that, 652 00:45:21,696 --> 00:45:24,473 therefore, amplitude modulation. 653 00:45:24,473 --> 00:45:28,773 So, for instance, if you looked at this signal as 654 00:45:28,773 --> 00:45:32,983 a function of time, then this would be the audio 655 00:45:32,983 --> 00:45:39,033 modulation of that signal. But the transmitter would 656 00:45:39,033 --> 00:45:43,078 transmit eight hundred fifty kiloHertz -- here, 657 00:45:43,078 --> 00:45:48,267 the signal would be a little stronger, here a little weaker, 658 00:45:48,267 --> 00:45:53,807 here a little stronger - and if this were a thousand Hertz tone, 659 00:45:53,807 --> 00:45:56,797 then this would be one millisecond. 660 00:45:56,797 --> 00:46:00,403 At the receiving end, you tune your radio, 661 00:46:00,403 --> 00:46:04,448 you change a capacitor somewhere in your radio, 662 00:46:04,448 --> 00:46:08,846 you have an LRC circuit, so that you 663 00:46:08,846 --> 00:46:13,895 are exactly on resonance at eight hundred fifty kiloHertz, 664 00:46:13,895 --> 00:46:18,589 and you're not on resonance at eight hundred and forty 665 00:46:18,589 --> 00:46:22,398 kiloHertz, so you don't hear other stations, 666 00:46:22,398 --> 00:46:27,89 but you really tune in on that one station, and you can receive 667 00:46:27,89 --> 00:46:31,256 this signal, then. And then you do some 668 00:46:31,256 --> 00:46:35,154 demodulation to only hear the audio envelope, 669 00:46:35,154 --> 00:46:38,52 and you hear speech and you hear music. 670 00:46:38,52 --> 00:46:43,978 That's the idea. Right here in twenty six one 671 00:46:43,978 --> 00:46:49,597 hundred, we have a transmitter, and I can transmit sound at 672 00:46:49,597 --> 00:46:52,988 almost any frequency that we choose. 673 00:46:52,988 --> 00:46:58,703 We have decided in honor of you, to transmit a one kiloHertz 674 00:46:58,703 --> 00:47:02,578 audio signal at eight zero two kiloHertz. 675 00:47:02,578 --> 00:47:06,163 The eight zero two is in honor of you. 676 00:47:06,163 --> 00:47:11,2 At eight hundred and two kiloHertz, there is no radio 677 00:47:11,2 --> 00:47:15,466 station, so this is a nice thing to do. 678 00:47:15,466 --> 00:47:17,814 We're not interfering with anyone. 679 00:47:17,814 --> 00:47:21,799 We're going to transmit it here, and then we have a radio 680 00:47:21,799 --> 00:47:26,353 here, and we are going to search for that signal at eight hundred 681 00:47:26,353 --> 00:47:29,697 and two kiloHertz. That's what we're going to do 682 00:47:29,697 --> 00:47:34,037 first before we're going to do some other things which are not 683 00:47:34,037 --> 00:47:36,385 so nice. Now, Marcos is an expert, 684 00:47:36,385 --> 00:47:40,868 in order to get the frequencies right, so Marcos has promised to 685 00:47:40,868 --> 00:47:42,86 help me with this, very nice. 686 00:47:42,86 --> 00:47:46,561 [tone] Oh, boy, you're already on, 687 00:47:46,561 --> 00:47:50,16 [laughs], we are already transmitting at eight hundred 688 00:47:50,16 --> 00:47:53,148 and two kiloHertz, and the station is already 689 00:47:53,148 --> 00:47:56,068 receiving it, the station meaning our radio. 690 00:47:56,068 --> 00:47:58,92 [tone] Marcos, let me convince the students 691 00:47:58,92 --> 00:48:01,229 that, indeed, [tone] that it -- oh, 692 00:48:01,229 --> 00:48:03,809 you changed the frequency. [tone] Yeah. 693 00:48:03,809 --> 00:48:06,322 [tone] So he changed the audio signal. 694 00:48:06,322 --> 00:48:10,328 [tone] So I want you [tone] to appreciate that we really are 695 00:48:10,328 --> 00:48:13,588 transmitting from this antenna, by unplugging it. 696 00:48:13,588 --> 00:48:16,779 [tone] [static] So now the radio doesn't see the 697 00:48:16,779 --> 00:48:21,956 electromagnetic waves, [tone] at eight hundred and two 698 00:48:21,956 --> 00:48:24,285 kiloHertz. [tone] So the radio is 699 00:48:24,285 --> 00:48:27,488 receiving now, [tone] the radio waves that we 700 00:48:27,488 --> 00:48:30,618 are producing. [tone] Now, we're going to do 701 00:48:30,618 --> 00:48:34,839 something that is not so nice. [tone] We're going to change 702 00:48:34,839 --> 00:48:38,187 our frequency to eight hundred fifty KiloHertz. 703 00:48:38,187 --> 00:48:42,7 [tone] So now what are we going to do is jamming the WEEA sport 704 00:48:42,7 --> 00:48:45,466 channel. [tone] So you may hear our one 705 00:48:45,466 --> 00:48:49,688 kiloHertz [tone] tone but you may not hear [tone] what they 706 00:48:49,688 --> 00:48:54,332 are saying. [tone] Can we first listen to 707 00:48:54,332 --> 00:48:58,002 WEEI, [tone] before we do this nasty thing? 708 00:48:58,002 --> 00:49:00,449 [tone] Radio: [static] Radio: 709 00:49:00,449 --> 00:49:03,681 uh, not the, you know, Larry Dominique 710 00:49:03,681 --> 00:49:09,186 matchup, but he says it was not -- now what -- what was the date 711 00:49:09,186 --> 00:49:13,555 of Clemens' -- This is WEEI? Radio: -- dig that up. 712 00:49:13,555 --> 00:49:17,137 Do we know the date? Now be a naughty boy. 713 00:49:17,137 --> 00:49:21,855 Radio: I've got all the, uh, the Celtics playoffs dates 714 00:49:21,855 --> 00:49:26,398 here -- [tone] We're doing something 715 00:49:26,398 --> 00:49:31,122 very illegal here. [tone] In fact, 716 00:49:31,122 --> 00:49:38,28 we can do even worse. [tone] I can be on the radio. 717 00:49:38,28 --> 00:49:44,864 [laughter] I'll have to turn off my microphone, 718 00:49:44,864 --> 00:49:51,449 because otherwise, you wouldn't know whether it 719 00:49:51,449 --> 00:49:58,32 comes from the radio, or whether it comes from my 720 00:49:58,32 --> 00:50:02,573 microphone. Hello, hello? 721 00:50:02,573 --> 00:50:05,545 Can you hear me? This is radio WHTL, 722 00:50:05,545 --> 00:50:09,195 it's a pirate station in the Cambridge area, 723 00:50:09,195 --> 00:50:13,865 we're now transmitting at eight hundred fifty kiloHertz. 724 00:50:13,865 --> 00:50:18,449 Our weekly programs will be on the latest excitement in 725 00:50:18,449 --> 00:50:21,761 science. Of course, we realize that this 726 00:50:21,761 --> 00:50:25,751 is illegal as hell, [laughter] but that's why we 727 00:50:25,751 --> 00:50:29,571 like it so much. [laughter] We start our first 728 00:50:29,571 --> 00:50:33,397 program next Monday at ten AM, 729 00:50:33,397 --> 00:50:37,997 and if you have any questions, feel free to contact the 730 00:50:37,997 --> 00:50:41,404 Physics Department of Harvard University. 731 00:50:41,404 --> 00:50:44,215 [laughter] See you next Wednesday. 732 00:50:44,215 --> 50:49 [applause]