1 00:00:01,020 --> 00:00:03,647 - [Voiceover] Okay, so last time we saw that for an open 2 00:00:03,647 --> 00:00:06,653 open tube, or an open open pipe, 3 00:00:06,653 --> 00:00:08,410 a pipe where both ends were open, 4 00:00:08,779 --> 00:00:11,704 there only particular wavelengths that were allowed, 5 00:00:11,704 --> 00:00:14,734 because you had to have anti-nodes at both ends. 6 00:00:15,118 --> 00:00:16,617 So, you had that one. 7 00:00:17,447 --> 00:00:19,337 We had this one. 8 00:00:19,828 --> 00:00:21,017 We have this one, 9 00:00:21,017 --> 00:00:23,098 and we found the wavelength of all of these. 10 00:00:23,098 --> 00:00:24,924 Then, we realized, wait a minute 11 00:00:24,924 --> 00:00:26,369 we can write down a formula. 12 00:00:26,845 --> 00:00:28,732 For any possible wavelength, 13 00:00:28,978 --> 00:00:31,169 in an open open tube, 14 00:00:31,430 --> 00:00:36,430 and it depends only on the length of the tube L and N. 15 00:00:36,647 --> 00:00:39,352 N is which harmonic we're talking about. 16 00:00:39,352 --> 00:00:42,016 One is the fundamental, two is the second harmonic, 17 00:00:42,016 --> 00:00:44,833 three is the third harmonic, four and so on. 18 00:00:45,109 --> 00:00:47,601 This gave you ever possible wavelength. 19 00:00:47,877 --> 00:00:50,123 The questions is, can we do the same thing 20 00:00:50,123 --> 00:00:52,297 if we had an open closed end? 21 00:00:52,533 --> 00:00:54,138 What happens if one ends closed? 22 00:00:54,138 --> 00:00:56,383 What if we closed this end off, 23 00:00:56,752 --> 00:00:58,622 so that it's not open anymore. 24 00:00:59,022 --> 00:01:01,153 Well, let's do that right now. Here we go. 25 00:01:01,153 --> 00:01:02,950 Here's a closed end right here. 26 00:01:03,488 --> 00:01:05,156 This end is closed. 27 00:01:05,742 --> 00:01:07,952 This is more like a soda bottle, 28 00:01:07,952 --> 00:01:09,510 because this end would be open, 29 00:01:09,510 --> 00:01:12,476 the top that you drink out of and the bottoms closed off. 30 00:01:12,476 --> 00:01:13,498 We've got air inside. 31 00:01:13,498 --> 00:01:14,859 If you blow over the top, 32 00:01:14,859 --> 00:01:17,243 what possible frequencies, what possible wavelengths 33 00:01:17,243 --> 00:01:18,487 could you set up? 34 00:01:18,717 --> 00:01:19,813 Well, what do we know here? 35 00:01:19,813 --> 00:01:21,913 We know that this end, this air is open 36 00:01:22,266 --> 00:01:23,498 or this side is open, 37 00:01:23,498 --> 00:01:26,871 and so this air molecule can oscillate wildly. 38 00:01:26,871 --> 00:01:29,170 What type of node is that going to be? 39 00:01:29,170 --> 00:01:30,370 That's going to be an anti-node, 40 00:01:30,370 --> 00:01:31,901 since it can oscillate a lot. 41 00:01:32,177 --> 00:01:34,997 This end over here, these air molecules keeping 42 00:01:34,997 --> 00:01:36,029 bumping into the side. 43 00:01:36,029 --> 00:01:37,890 It's got to be a node over on this end, 44 00:01:37,890 --> 00:01:39,811 because there can't be any displacement. 45 00:01:40,780 --> 00:01:42,039 What do we do here? 46 00:01:42,039 --> 00:01:43,482 This ends a node. 47 00:01:44,020 --> 00:01:46,448 We know that. I'm going to put this on the axis here. 48 00:01:46,448 --> 00:01:48,486 I know this end has no displacement. 49 00:01:48,486 --> 00:01:51,182 We're graphing displacement again versus X. 50 00:01:51,182 --> 00:01:53,599 This is, in this case, horizontal displacement. 51 00:01:53,983 --> 00:01:55,405 This end is going to oscillate wildly, 52 00:01:55,405 --> 00:01:56,801 so I know there's going to be an anti-node. 53 00:01:56,801 --> 00:01:58,218 So, I'm going to put it right here. 54 00:01:58,971 --> 00:02:01,163 I'm going to draw the simplest possible wave 55 00:02:01,163 --> 00:02:02,869 that can go from this anti-node 56 00:02:02,869 --> 00:02:05,817 to this node is going to look like this. 57 00:02:06,278 --> 00:02:09,514 Anti-node and it goes curve right down to the node. 58 00:02:09,514 --> 00:02:10,353 That's it. 59 00:02:10,353 --> 00:02:11,976 What wavelength is this? 60 00:02:11,976 --> 00:02:14,219 Well, in terms of the length of this tube, 61 00:02:15,910 --> 00:02:17,229 so if this is L, 62 00:02:18,382 --> 00:02:21,081 what wavelength is this in terms of L? 63 00:02:21,773 --> 00:02:23,876 We've got to figure out how much of a wavelength this is. 64 00:02:23,876 --> 00:02:26,944 That's always the trick. This is what freaks students out. 65 00:02:26,944 --> 00:02:30,243 They don't like figuring out how many wavelengths is this. 66 00:02:30,243 --> 00:02:31,597 It's not too hard. 67 00:02:31,858 --> 00:02:33,643 First thing I like to do is draw 68 00:02:33,950 --> 00:02:36,173 what I know one wavelength looks like. 69 00:02:36,173 --> 00:02:38,197 So, what does one wavelength look like? 70 00:02:38,689 --> 00:02:40,455 One wavelength looks like this. 71 00:02:40,455 --> 00:02:41,504 If we start up here, 72 00:02:42,365 --> 00:02:44,100 a wavelength is going all the way 73 00:02:44,100 --> 00:02:46,902 and then back to the same point in the process. 74 00:02:46,902 --> 00:02:50,078 There we go. That's one entire wavelength, 75 00:02:50,078 --> 00:02:53,195 at least if this is a versus X graph it is. 76 00:02:53,810 --> 00:02:55,895 So, how much of a wavelength is this pink line 77 00:02:55,895 --> 00:02:58,131 for this first fundamental frequency? 78 00:02:58,131 --> 00:02:59,651 This first fundamental wavelength? 79 00:02:59,651 --> 00:03:02,211 It starts at the top, so let's start at the top. 80 00:03:02,211 --> 00:03:05,341 It goes, and that thing just goes till the first 81 00:03:05,617 --> 00:03:08,142 crossing of the axis, and that's the node. 82 00:03:08,142 --> 00:03:10,207 So, this thing crosses the axis here. That's it. 83 00:03:10,207 --> 00:03:12,353 That's all we got. We got a big long ... 84 00:03:12,845 --> 00:03:15,300 what is this? This is one-fourth of a wavelength. 85 00:03:15,300 --> 00:03:17,825 That's one-fourth, and it goes to here. 86 00:03:17,825 --> 00:03:19,351 That's another fourth. 87 00:03:19,351 --> 00:03:21,586 Here's another fourth, and here's another fourth. 88 00:03:21,586 --> 00:03:23,886 So, this is only one-fourth of a wavelength. 89 00:03:24,686 --> 00:03:26,430 That's hard for a lot of people to see. 90 00:03:26,430 --> 00:03:29,035 The whole things one wavelength. 91 00:03:29,035 --> 00:03:31,755 Half of it is a half, so if I cut it in half, 92 00:03:31,755 --> 00:03:34,320 that's a half, and I cut this half in half again, 93 00:03:34,320 --> 00:03:35,833 I get one-fourth. 94 00:03:35,833 --> 00:03:37,789 So, what I find out is that, okay, 95 00:03:37,789 --> 00:03:41,252 the length L equals one-fourth 96 00:03:41,252 --> 00:03:42,873 of a wavelength in this case. 97 00:03:42,873 --> 00:03:45,712 Our fundamental wavelength divided by four 98 00:03:45,712 --> 00:03:47,856 equals the length of this tube. 99 00:03:47,856 --> 00:03:49,914 So, if I want to know what the wavelength is, 100 00:03:49,914 --> 00:03:52,434 that means my wavelength for the fundamental 101 00:03:52,434 --> 00:03:54,990 open closed case is four L. 102 00:03:55,405 --> 00:03:56,603 I'm going to write that over here. 103 00:03:56,603 --> 00:03:59,797 (Lambda) equals four L, 104 00:03:59,797 --> 00:04:02,763 and this would be the fundamental wavelength 105 00:04:04,623 --> 00:04:06,688 for this open closed tube. 106 00:04:06,688 --> 00:04:07,628 This is bigger. 107 00:04:07,628 --> 00:04:10,896 For open open is was two L, so it's four L. 108 00:04:10,896 --> 00:04:11,934 How about the next one? 109 00:04:11,934 --> 00:04:14,084 All right, we got it started in the anti-node, 110 00:04:14,084 --> 00:04:15,474 and we got it into the node. 111 00:04:15,474 --> 00:04:17,540 The next simplest case in ... 112 00:04:17,540 --> 00:04:19,384 well, we had no nodes in between. 113 00:04:19,384 --> 00:04:20,720 We only had one at the end. 114 00:04:20,720 --> 00:04:22,393 So, now I need a node in the middle. 115 00:04:22,393 --> 00:04:25,174 I'm going to create a node in the middle, 116 00:04:25,174 --> 00:04:26,773 and then I have to get all the way back 117 00:04:26,773 --> 00:04:29,512 to the node on this end. 118 00:04:29,512 --> 00:04:32,328 So, I've got one node here. I've got a node at the end. 119 00:04:32,774 --> 00:04:35,370 I've got this anti-node here, and an anti-node up here. 120 00:04:35,370 --> 00:04:37,434 How many wavelengths is this? 121 00:04:37,434 --> 00:04:39,054 Let's figure it out. Start at the top. 122 00:04:39,730 --> 00:04:41,281 All right, this goes all the way down 123 00:04:41,281 --> 00:04:42,769 past the node and back up. 124 00:04:42,769 --> 00:04:45,642 So, all the way down, past the node, 125 00:04:45,642 --> 00:04:47,725 back up, and ends at a node. 126 00:04:47,725 --> 00:04:49,478 That's how much of a wavelength I've got here . 127 00:04:50,231 --> 00:04:51,005 So, how much is this? 128 00:04:51,005 --> 00:04:54,676 Well, it's one-fourth, two-fourths, three-fourths. 129 00:04:54,999 --> 00:04:57,687 This time L is the length of my tube. 130 00:04:57,687 --> 00:05:00,046 Is my wavelengths fitting into L? 131 00:05:00,046 --> 00:05:02,969 In this case, it's three-fourths of a wavelength. 132 00:05:03,769 --> 00:05:05,709 Again, if I solved that for wavelength, 133 00:05:05,709 --> 00:05:09,538 I'd get four L over three. 134 00:05:10,353 --> 00:05:13,530 So, the next possible wavelength is 135 00:05:13,530 --> 00:05:16,026 four L over three. 136 00:05:17,779 --> 00:05:19,397 If we solve for the next one, 137 00:05:19,397 --> 00:05:21,361 let's draw it, started an anti-node, 138 00:05:21,361 --> 00:05:23,256 end a node, the next possible one, 139 00:05:23,256 --> 00:05:24,806 well, the last one had one node, 140 00:05:24,806 --> 00:05:26,153 this time it's going to have two nodes. 141 00:05:26,153 --> 00:05:27,303 I'm going to come down here. 142 00:05:27,612 --> 00:05:30,102 One node, two node, 143 00:05:30,102 --> 00:05:32,245 and then it gets (back) to the node at the end. 144 00:05:32,245 --> 00:05:34,803 So, a node at this end, there has to be a node at this end, 145 00:05:34,803 --> 00:05:35,784 because it's closed. 146 00:05:35,784 --> 00:05:37,827 This time I have two nodes in the middle. 147 00:05:38,549 --> 00:05:40,010 I have a anti-node on this end, 148 00:05:40,010 --> 00:05:41,159 and two anti-nodes in the middle. 149 00:05:41,159 --> 00:05:43,130 So, how many wavelengths is this? 150 00:05:43,130 --> 00:05:44,259 All right, let's figure it out. 151 00:05:44,259 --> 00:05:45,401 Start at the top. 152 00:05:45,877 --> 00:05:48,324 All right, it comes down, let's just trace it out. 153 00:05:48,324 --> 00:05:51,149 Down, hits that first node, 154 00:05:51,702 --> 00:05:53,399 down to the anti-node, 155 00:05:53,399 --> 00:05:55,858 back up to the node, now, I've gotten to here. 156 00:05:56,565 --> 00:05:59,382 I keep going. I go up to the top, I'm not done yet. 157 00:05:59,382 --> 00:06:00,838 Now, I'm back up to here. 158 00:06:00,838 --> 00:06:04,542 I have to keep going one more fourth of a wavelength. 159 00:06:05,065 --> 00:06:06,789 This is more than a wavelength. 160 00:06:06,789 --> 00:06:09,247 This time L equals, 161 00:06:09,662 --> 00:06:12,916 well, this is one whole wavelength just to this 162 00:06:12,916 --> 00:06:14,444 point right here. 163 00:06:15,044 --> 00:06:16,793 Then, I have to add one more fourth 164 00:06:16,793 --> 00:06:18,040 of a wavelength to that. 165 00:06:18,040 --> 00:06:20,050 So, this is one wavelength and a fourth, 166 00:06:20,050 --> 00:06:21,362 or another way to say that is that 167 00:06:21,362 --> 00:06:24,281 this is five-fourths of a wavelength. 168 00:06:25,220 --> 00:06:26,291 Five-fourths of a wavelength. 169 00:06:26,291 --> 00:06:30,261 Just to here is one whole wavelength, 170 00:06:30,261 --> 00:06:31,829 and I have to add one more fourth to that. 171 00:06:32,167 --> 00:06:34,515 So, if I solve for lambda, I get lambda is 172 00:06:34,515 --> 00:06:36,720 four L, ... we see a pattern. 173 00:06:37,212 --> 00:06:39,817 Patters are great. Four L over five. 174 00:06:40,201 --> 00:06:44,283 This next wavelength possible is four L over five 175 00:06:44,283 --> 00:06:47,514 and shoot, we can do this now. 176 00:06:47,514 --> 00:06:48,516 Now, I see enough. 177 00:06:48,516 --> 00:06:50,915 If I want to write down any possible wavelength, 178 00:06:51,515 --> 00:06:52,733 it's going to be four L. 179 00:06:52,733 --> 00:06:55,057 Look, four L, four L over three, four L over five. 180 00:06:55,057 --> 00:06:56,885 The next one four L over seven. 181 00:06:57,438 --> 00:06:59,220 I get that the possible wavelengths for 182 00:06:59,220 --> 00:07:02,469 an open closed tube are four L over N. 183 00:07:02,469 --> 00:07:06,992 Except, instead of being any possible integer, 184 00:07:07,776 --> 00:07:10,737 the only allowed integers are the odd ones. 185 00:07:11,537 --> 00:07:14,626 So, I'm not allowed to put in two or four. 186 00:07:14,626 --> 00:07:17,970 It's got to be one, three, five, and so on. 187 00:07:19,200 --> 00:07:21,009 Here's the formula. This is it. 188 00:07:21,009 --> 00:07:22,757 If I want to know what are the possible wavelengths 189 00:07:22,757 --> 00:07:25,080 allowed in an open closed tube, 190 00:07:25,695 --> 00:07:28,506 this is it. It depends on the length. It depends on N. 191 00:07:29,182 --> 00:07:31,318 Looks just like the case for open open, 192 00:07:31,748 --> 00:07:34,440 except it was two L for that case. 193 00:07:34,440 --> 00:07:36,064 This case is four L on top. 194 00:07:36,064 --> 00:07:37,395 Four times length of the tube, 195 00:07:37,395 --> 00:07:39,949 and on the bottom it's only the odd integers. 196 00:07:39,949 --> 00:07:41,932 That means I only get the odd harmonics. 197 00:07:41,932 --> 00:07:43,325 This four L over three, 198 00:07:43,325 --> 00:07:45,266 I wouldn't call this the second harmonic, 199 00:07:45,266 --> 00:07:47,256 I'd call this the third harmonic. 200 00:07:47,871 --> 00:07:50,156 This five down here, I wouldn't call this the third, 201 00:07:50,156 --> 00:07:51,381 I'd call this the fifth. 202 00:07:51,381 --> 00:07:56,381 We're missing all the even harmonics on this case 203 00:07:56,450 --> 00:07:58,012 for an open closed tube. 204 00:07:58,012 --> 00:07:59,196 It's a little bit strange, 205 00:07:59,196 --> 00:08:00,351 but that's what happens when you have an 206 00:08:00,351 --> 00:08:01,860 anti-node at this end, 207 00:08:01,860 --> 00:08:04,193 and a node required at that end. 208 00:08:05,269 --> 00:08:07,607 You can try this. Look, this is a function of L. 209 00:08:08,160 --> 00:08:09,373 If you want to test this out, 210 00:08:09,373 --> 00:08:10,610 next time you're drinking a soda. 211 00:08:10,610 --> 00:08:12,937 Look, if the L is large 212 00:08:12,937 --> 00:08:14,885 if the length of your tube is large, 213 00:08:15,054 --> 00:08:17,415 that means the wavelength should be large. 214 00:08:17,415 --> 00:08:19,332 If the wavelength is large, 215 00:08:19,332 --> 00:08:20,461 well, let's see. 216 00:08:20,461 --> 00:08:22,178 V equals lambda F. 217 00:08:23,239 --> 00:08:24,889 If you've got a big wavelength, 218 00:08:25,135 --> 00:08:26,934 that'll mean a small frequency, 219 00:08:26,934 --> 00:08:28,724 because the speed won't change. 220 00:08:28,724 --> 00:08:30,671 The speeds determined by the medium, 221 00:08:30,671 --> 00:08:32,960 and you're probably not changing the temperature 222 00:08:32,960 --> 00:08:34,485 of the medium all that much. 223 00:08:34,485 --> 00:08:36,341 Maybe, you've got ice in your drink or something, 224 00:08:36,341 --> 00:08:38,942 but if it melts it'll change a little bit. 225 00:08:38,942 --> 00:08:41,076 It's not going to change the speed by that much. 226 00:08:41,076 --> 00:08:42,909 If you increase the length, 227 00:08:42,909 --> 00:08:43,956 you'll increase the wavelength, 228 00:08:43,956 --> 00:08:45,165 it'll decrease the frequency. 229 00:08:45,165 --> 00:08:47,594 Low frequency means a low note. 230 00:08:47,594 --> 00:08:50,053 You'll hear a lower bassy note. 231 00:08:50,053 --> 00:08:52,218 Try this, I want you to try this out 232 00:08:52,218 --> 00:08:53,632 the next time you're drinking a soda, 233 00:08:54,908 --> 00:08:56,935 or maybe it's a healthy beverage. 234 00:08:58,011 --> 00:08:59,059 Whatever it is. 235 00:08:59,059 --> 00:09:01,717 You got some soda here, it's up to some level. 236 00:09:03,809 --> 00:09:06,642 Where ever the waters at acts as the bottom of the tube. 237 00:09:06,642 --> 00:09:08,931 Right now, I only have a tube this length. 238 00:09:10,131 --> 00:09:11,312 The top is open, 239 00:09:11,312 --> 00:09:13,508 and the bottom is basically where ever 240 00:09:13,508 --> 00:09:14,555 there's water level is, 241 00:09:14,555 --> 00:09:17,018 because the air can't get past that water level. 242 00:09:17,018 --> 00:09:18,434 This would only be a length of that. 243 00:09:18,434 --> 00:09:19,642 As you keep drinking, 244 00:09:20,057 --> 00:09:21,665 keep blowing over the top. 245 00:09:22,634 --> 00:09:23,846 As you keep blowing over the top, 246 00:09:23,846 --> 00:09:25,422 listen for what note you hear. 247 00:09:25,422 --> 00:09:27,337 You should keep hearing a lower note. 248 00:09:27,875 --> 00:09:30,623 The lower this gets, once it's down to here, 249 00:09:31,192 --> 00:09:32,678 now your length ... 250 00:09:32,998 --> 00:09:35,063 the length of your tube is bigger. 251 00:09:35,063 --> 00:09:36,770 It's open at the top closed at the bottom. 252 00:09:36,770 --> 00:09:38,088 You'll hear even a lower note, 253 00:09:38,088 --> 00:09:39,251 once it gets down to here. 254 00:09:39,251 --> 00:09:40,341 When you finish, 255 00:09:40,940 --> 00:09:42,527 now it's even longer. 256 00:09:42,527 --> 00:09:44,126 You'll hear a much lower notes. 257 00:09:44,126 --> 00:09:45,878 The notes should get lower and lower. 258 00:09:46,524 --> 00:09:48,596 Not louder and louder, but lower and lower, 259 00:09:48,596 --> 00:09:50,861 the frequency should sound lower and lower 260 00:09:51,384 --> 00:09:52,751 the lower your drink gets. 261 00:09:52,751 --> 00:09:54,844 The higher the length, bigger the wavelength, 262 00:09:54,844 --> 00:00:00,000 smaller the frequency.