1
00:00:28,000 --> 00:00:33,630
I will summarize what we have learned about the 2
00:00:33,630 --> 00:00:37,990
normal modes of a string fixed at both ends which is 3
00:00:37,990 --> 00:00:41,710
very relevant today for musical instruments. 4
00:00:41,710 --> 00:00:48,850
Suppose I have a string with length L, mass for unit length μ and tension T. 5
00:00:48,850 --> 00:00:50,540
Then I know that the speed 6
00:00:50,540 --> 00:00:56,160
of propagation is the squar root of T devided by μ. 7
00:00:56,160 --> 00:01:02,270
And the wave length is always the speed of propagation 8
00:01:02,270 --> 00:01:04,290
devided by the frequency. 9
00:01:04,290 --> 00:01:07,360
Speed of the propagation times the period of one 10
00:01:07,360 --> 00:01:12,520
osillation but I avoid capital tease for period 11
00:01:12,520 --> 00:01:15,970
so I would write it down as frequency. 12
00:01:15,970 --> 00:01:22,020
And so in its lowest mode we call that fundamental 13
00:01:22,020 --> 00:01:28,270
first harmonic you will get then this situation n equals 1 14
00:01:28,270 --> 00:01:34,390
and λ1 is then clearly 2L and this length is L and the 15
00:01:34,390 --> 00:01:44,410
frequency is then v devided by 2L for that's the frequency 16
00:01:44,410 --> 00:01:51,860
for the lowest possible mode, first harmonic. 17
00:01:51,860 --> 00:01:57,430
If we go to the second harmonic then the picture changes, 18
00:01:57,430 --> 00:02:02,880
we get a node in the middle and so we have here n equals 2. 19
00:02:02,880 --> 00:02:12,670
So λ2 is now L and so f2 is now again v devided by the 20
00:02:12,670 --> 00:02:17,910
wave length so it becomes now v devided by L. 21
00:02:17,910 --> 00:02:22,140
And so we can write down now the general equation 22
00:02:22,140 --> 00:02:31,550
for the nth-mode and being nancy (?) of n is then 2L devided by n, 23
00:02:31,550 --> 00:02:35,160
and the frequency in the nth-mode which is the 24
00:02:35,160 --> 00:02:41,010
nth-harmonic is then nv devided by 2L. 25
00:02:41,010 --> 00:02:46,120
And this v is given there. 26
00:02:46,120 --> 00:02:49,240
So what you see here that is the fundamental here 27
00:02:49,240 --> 00:02:52,910
where for instance 100 Hz then the second harmonic 28
00:02:52,910 --> 00:02:57,860
would be 200 Hz, the third harmonic 300 Hz, they come 29
00:02:57,860 --> 00:03:03,260
in series one, two, three, four, five and so on. 30
00:03:03,260 --> 00:03:08,500
Now clearly there is the possibility that I will have 31
00:03:08,500 --> 00:03:11,460
one end of that string open, 32
00:03:11,460 --> 00:03:15,270
we call this then closed-closed or fixed-fixed. 33
00:03:15,270 --> 00:03:18,050
We suppose I have the same length L, 34
00:03:18,050 --> 00:03:23,950
so here I have this infamous rod which is frictionless with the infamous ring 35
00:03:23,950 --> 00:03:25,540
which has no mass. 36
00:03:25,540 --> 00:03:28,120
And it is fixed here and now I want to know 37
00:03:28,120 --> 00:03:30,940
what the normal modes are and then in the lowest 38
00:03:30,940 --> 00:03:34,330
mode you get this, 39
00:03:34,330 --> 00:03:37,570
this angule is 90 degrees the why the x must be zero there. 40
00:03:37,570 --> 00:03:41,260
And then it oscillates like this, back and forth. 41
00:03:41,260 --> 00:03:44,420
And so now you have that n equals 1 which is 42
00:03:44,420 --> 00:03:47,690
now the fundamental first harmonic, 43
00:03:47,690 --> 00:03:55,180
λ1 is now 4L, λ1. 44
00:03:55,180 --> 00:03:57,970
And there for the frequency that you now generate 45
00:03:57,970 --> 00:04:04,450
is twice as low as now v devided by 4L. 46
00:04:04,450 --> 00:04:06,750
So you can go one step further. 47
00:04:06,750 --> 00:04:10,260
You can ask now for the second harmonic. 48
00:04:10,260 --> 00:04:13,040
So here again is that rod, 49
00:04:13,040 --> 00:04:16,820
so now I introduce another node here, 50
00:04:16,820 --> 00:04:19,880
and so now the string would look like this. 51
00:04:19,880 --> 00:04:23,420
This is again 90 degrees and as it oscillates 52
00:04:23,420 --> 00:04:25,670
it would move like this. 53
00:04:25,670 --> 00:04:27,350
And so now this is n equals 2. 54
00:04:27,350 --> 00:04:30,730
This is the second harmonic. 55
00:04:30,730 --> 00:04:32,880
You can just look at it λ2, 56
00:04:32,880 --> 00:04:37,320
it's four-thirds times L, Right? 57
00:04:37,320 --> 00:04:39,050
You need to fit it longer. 58
00:04:39,050 --> 00:04:51,270
And therefore f2 is now three devided by, 3v devided by 4L. 59
00:04:51,270 --> 00:04:54,290
And so now we can write down the general recipe 60
00:04:54,290 --> 00:04:57,780
for the nth-mode and being nancy. 61
00:04:57,780 --> 00:05:12,190
So we will find then that λn is now 4L devided by 2n-1. 62
00:05:12,190 --> 00:05:16,850
And that now changes the picture quite dramatically. 63
00:05:16,850 --> 00:05:22,060
Coz if you follow here that you go from λ1 to λ2 64
00:05:22,060 --> 00:05:28,760
it changes not by a factor of 2 but it changes by a factor of 3. 65
00:05:28,760 --> 00:05:32,900
And so the frequency in the nth-mode 66
00:05:32,900 --> 00:05:40,510
which is the velocity devided by λn is 2n-1 times 67
00:05:40,510 --> 00:05:46,090
velocity devided by 4L (see the black board). 68
00:05:46,090 --> 00:05:49,600
And so what you see now if we take both systems 69
00:05:49,600 --> 00:05:51,420
and suppose L were the same, 70
00:05:51,420 --> 00:05:54,040
μ were the same and T were the same, 71
00:05:54,040 --> 00:05:57,650
then f1 in this mode, 72
00:05:57,650 --> 00:06:01,910
this instrument is half the frequency of f1 there, 73
00:06:01,910 --> 00:06:04,420
because there you have downstairs of 2L, 74
00:06:04,420 --> 00:06:08,330
and here you have a 4L. 75
00:06:08,330 --> 00:06:11,620
So for instance if that were 100 Hz, 76
00:06:11,620 --> 00:06:13,830
with the same length here, 77
00:06:13,830 --> 00:06:15,600
you would get 50 Hz, 78
00:06:15,600 --> 00:06:17,510
all L and other things are the same. 79
00:06:17,510 --> 00:06:20,620
And then the second harmonic will be 150 Hz, 80
00:06:20,620 --> 00:06:22,810
because if n becomes 1, 81
00:06:22,810 --> 00:06:24,120
you get 3 upstairs, 82
00:06:24,120 --> 00:06:25,280
if n becomes 2, 83
00:06:25,280 --> 00:06:26,340
you get 5 upstairs. 84
00:06:26,340 --> 00:06:30,330
So now the ratio is 1, 3, 5, 7. 85
00:06:30,330 --> 00:06:34,240
For as there the ratio is 1, 2, 3, 4, etc. 86
00:06:34,240 --> 00:06:40,190
Now if I take a string in isolation, 87
00:06:40,190 --> 00:06:43,120
and I oscillate it, I almost hear no sounds. 88
00:06:43,120 --> 00:06:47,160
Because not enough air that is displaced by the string. 89
00:06:47,160 --> 00:06:50,030
And so what we do is we have to mount it 90
00:06:50,030 --> 00:06:53,530
on a surface that starts to fiberate with it. 91
00:06:53,530 --> 00:06:57,520
And you see that own all musical instruments. 92
00:06:57,520 --> 00:06:59,460
I will demonstrate that to you in a simple 93
00:06:59,460 --> 00:07:01,760
way with a tuning fork. 94
00:07:01,760 --> 00:07:05,630
I have here a tuning fork and if I just excite 95
00:07:05,630 --> 00:07:08,250
this tuning fork and it's 440 Hz, 96
00:07:08,250 --> 00:07:10,690
you will hear practically nothing. 97
00:07:10,690 --> 00:07:14,260
I hit it now. 98
00:07:14,260 --> 00:07:15,830
I can hear it. I am very close. 99
00:07:15,830 --> 00:07:17,810
But most of you cannot hear. 100
00:07:17,810 --> 00:07:19,900
However the moment I put it on the surface, 101
00:07:19,900 --> 00:07:21,920
the surface starts to fiberate with it, 102
00:07:21,920 --> 00:07:25,700
so I drain the energy faster out of the tuning fork, 103
00:07:25,700 --> 00:07:28,050
but you get more volume, more sound. 104
00:07:28,050 --> 00:07:29,810
Larger surface oscillates, 105
00:07:29,810 --> 00:07:32,070
so the pressure wave is stronger. 106
00:07:32,070 --> 00:07:40,270
And I will demonstrate that. 107
00:07:40,270 --> 00:07:42,680
You hear it now? 108
00:07:42,680 --> 00:07:48,190
Do you hear? 109
00:07:48,190 --> 00:07:49,870
Big difference, right? 110
00:07:49,870 --> 00:07:52,660
Huge difference when I put it on the surface. 111
00:07:52,660 --> 00:07:57,110
I have here a music box which I bought many years 112
00:07:57,110 --> 00:08:00,630
ago in Austria and has these planks, 113
00:08:00,630 --> 00:08:01,590
and when I rotate it, 114
00:08:01,590 --> 00:08:04,490
I may be able to hear with but you won't hear it. 115
00:08:04,490 --> 00:08:08,150
Maybe some of you very close. 116
00:08:08,150 --> 00:08:09,630
Can you hear it? 117
00:08:09,630 --> 00:08:11,010
Good for you. 118
00:08:11,010 --> 00:08:16,790
Now listen. 119
00:08:16,790 --> 00:08:19,230
Big difference. 120
00:08:19,230 --> 00:08:20,840
Now the whole surface oscillates, 121
00:08:20,840 --> 00:08:22,940
again you drain the energy faster of course, 122
00:08:22,940 --> 00:08:25,950
but you get more sounds and I put it on here. 123
00:08:37,300 --> 00:08:39,320
Big difference. 124
00:08:39,320 --> 00:08:41,960
And of course you will see that in the design of 125
00:08:41,960 --> 00:08:44,330
all musical instruments. 126
00:08:44,330 --> 00:08:48,470
Needless to say that the design of the sounding 127
00:08:48,470 --> 00:08:51,090
boards which are connected to the strings. 128
00:08:51,090 --> 00:08:53,830
I of course secret that the company 129
00:08:53,830 --> 00:08:56,970
are very fond of, often not telling you. 130
00:09:00,230 --> 00:09:02,920
I am not aware of musical instruments of string 131
00:09:02,920 --> 00:09:06,930
instruments where by one end of the string 132
00:09:06,930 --> 00:09:10,870
is attached to a frictionless rod and whereby that 133
00:09:10,870 --> 00:09:14,740
end is attached to a massless ring. 134
00:09:14,740 --> 00:09:18,360
So I will restrict myself in discussing musical 135
00:09:18,360 --> 00:09:20,310
instruments, string instruments, to the one 136
00:09:20,310 --> 00:09:24,210
whereby both ends are fixed. 137
00:09:24,210 --> 00:09:28,600
And so therefore the frequency f1, 138
00:09:28,600 --> 00:09:33,190
that is the one that I'm interested in is the speed of propagation 139
00:09:33,190 --> 00:09:38,870
which is T devided by μ and then 1 devided by 2L. 140
00:09:38,870 --> 00:09:42,650
So these are the key players in the design of the instruments. 141
00:09:42,650 --> 00:09:44,850
If you make L longer, you get a lower pitch. 142
00:09:44,850 --> 00:09:47,380
If you make L shorter, you get a higher pitch. 143
00:09:47,380 --> 00:09:49,160
We all know that you make L shorter, 144
00:09:49,160 --> 00:09:50,450
you get a higher pitch 145
00:09:50,450 --> 00:09:52,490
If you make the tension higher, 146
00:09:52,490 --> 00:09:55,240
you get a higher pitch. 147
00:09:55,240 --> 00:09:57,290
If you make the mass of a unit length lower, 148
00:09:57,290 --> 00:09:59,070
you get a higher pitch. 149
00:09:59,070 --> 00:10:01,380
So that's key in designing musical instruments. 150
00:10:01,380 --> 00:10:03,280
If you take a piano, 151
00:10:03,280 --> 00:10:05,000
It has 88 keys, 152
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the lowest frequency is 28 Hz, 153
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the highest is 4000 Hz. 154
00:10:09,540 --> 00:10:11,960
It covers seven octaves. 155
00:10:11,960 --> 00:10:13,950
And when you hit a key, you... 156
00:10:13,950 --> 00:10:18,770
the hammer actually comes down onto the string, 157
00:10:18,770 --> 00:10:23,840
and it excites the string in the common nation of various normal modes. 158
00:10:23,840 --> 00:10:26,390
In fact, in many cases when you hit one key without 159
00:10:26,390 --> 00:10:29,790
you realizing it, you hit more than one string simultaneously, 160
00:10:29,790 --> 00:10:32,660
but that 's the detail now which I will not further expand on. 161
00:10:32,660 --> 00:10:35,890
If you take a Steinway(?) grand piano, 162
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even though there are only 88 keys, 163
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it has two hundred and sixteen strings. 164
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And so the idea of piano then is that you 165
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change the length of the strings. 166
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That's a player. 167
00:10:48,430 --> 00:10:49,410
Shorter the length, 168
00:10:49,410 --> 00:10:50,830
the higher the frequency. 169
00:10:50,830 --> 00:10:52,180
And you can change μ. 170
00:10:52,180 --> 00:10:53,950
When you open the piano and you look at 171
00:10:53,950 --> 00:10:56,110
the various strings you merely see 172
00:10:56,110 --> 00:10:58,400
that some strings are as thick as my pinkie, 173
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we have a huge μ and the others are very thin 174
00:11:00,720 --> 00:11:02,630
they have a very low value for μ. 175
00:11:02,630 --> 00:11:06,160
That will give you then a higher pitch. 176
00:11:06,160 --> 00:11:10,200
The tension of the strings in a piano 177
00:11:10,200 --> 00:11:12,020
are approximately all the same. 178
00:11:12,020 --> 00:11:13,430
They are quite high, 179
00:11:13,430 --> 00:11:16,500
They are near 200N per string. 180
00:11:16,500 --> 00:11:17,990
So a grand piano, 181
00:11:17,990 --> 00:11:19,750
then the total force all the 182
00:11:19,750 --> 00:11:22,580
strings together is something like 4500N. 183
00:11:22,580 --> 00:11:26,970
It is an immense force when you think about that. 184
00:11:26,970 --> 00:11:29,290
Now we go to violins and cello and bass, 185
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they have four strings. 186
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Then the length is a given. 187
00:11:33,300 --> 00:11:35,350
But if you look at the various strings, 188
00:11:35,350 --> 00:11:36,770
and we will you see a violin later, 189
00:11:36,770 --> 00:11:39,010
you will see that one string is much thicker 190
00:11:39,010 --> 00:11:39,760
than the other. 191
00:11:39,760 --> 00:11:40,920
So you play with μ, 192
00:11:40,920 --> 00:11:43,500
change the μ. 193
00:11:43,500 --> 00:11:47,580
So you only have four fundmentals then. 194
00:11:47,580 --> 00:11:50,400
If you go to a museum of fine arts in Boston, 195
00:11:50,400 --> 00:11:53,330
they have wonderful collction of musical instruments. 196
00:11:53,330 --> 00:11:55,180
You will see musical instruments with just 197
00:11:55,180 --> 00:11:57,580
two strings and you will also see musical 198
00:11:57,580 --> 00:12:00,600
instruments with one string but I have never 199
00:12:00,600 --> 00:12:04,360
seen one I said earlier will by one end of the string, 200
00:12:04,360 --> 00:12:05,840
it can freely move. 201
00:12:05,840 --> 00:12:08,520
But maybe they do exist. 202
00:12:08,520 --> 00:12:11,510
So now comes the issue if you have built instrument, 203
00:12:11,510 --> 00:12:12,640
how do you tone it? 204
00:12:12,640 --> 00:12:15,360
Well, with a piano, you ask a piano toner, 205
00:12:15,360 --> 00:12:16,250
maybe once a year, 206
00:12:16,250 --> 00:12:19,050
once every year to come and tone the piano for you. 207
00:12:19,050 --> 00:12:20,290
And what the piano toner does, 208
00:12:20,290 --> 00:12:23,360
he simply changes the tension in the strings, 209
00:12:23,360 --> 00:12:24,680
which is a major job of course if you have 210
00:12:24,680 --> 00:12:27,790
two hundred and sixteen strings. 211
00:12:27,790 --> 00:12:31,390
As with a violin and a guitar and a cello and a bass, 212
00:12:31,390 --> 00:12:36,000
it is the player herself or himself who is doing the toning. 213
00:12:36,000 --> 00:12:37,750
We will see that later today. 214
00:12:37,750 --> 00:12:40,280
They actually change the tension in the string 215
00:12:40,280 --> 00:12:44,820
and they listen carefully to get just the right tone. 216
00:12:44,820 --> 00:12:49,590
And they do that before they start playing. 217
00:12:49,590 --> 00:12:52,710
If you play the piano, 218
00:12:52,710 --> 00:12:54,730
with all do respectful piano players, 219
00:12:54,730 --> 00:12:57,100
all they have to do is hit the right keys in the right sequence. 220
00:12:57,100 --> 00:12:59,970
That's orders as tunes when you are a piano player. 221
00:12:59,970 --> 00:13:05,250
Now think about a violinist or a guitar or a cello, 222
00:13:05,250 --> 00:13:08,710
they cannot just hit one string. 223
00:13:08,710 --> 00:13:14,460
They have to change the lengths of the string all the time, 224
00:13:14,460 --> 00:13:16,160
to change the fundamental, 225
00:13:16,160 --> 00:13:18,600
and that's the whole idea when have the violin, 226
00:13:18,600 --> 00:13:20,610
and you strike it with a bow, 227
00:13:20,610 --> 00:13:23,040
you rub the string and the string was to start to oscillate 228
00:13:23,040 --> 00:13:24,900
in the fundamental and higher harmonic. 229
00:13:24,900 --> 00:13:27,580
By making the string now shorter with your hands, 230
00:13:27,580 --> 00:13:29,060
you increase the pitch. 231
00:13:29,060 --> 00:13:31,980
And so playing there is that you as a player, 232
00:13:31,980 --> 00:13:35,720
continuously have to move the length of the string, 233
00:13:35,720 --> 00:13:38,470
and just hit the right length. 234
00:13:38,470 --> 00:13:39,820
Because beyond my imagination, 235
00:13:39,820 --> 00:13:41,090
that anyone can do that. 236
00:13:41,090 --> 00:13:44,110
I cannot. I tried it when I was joined to a violin lessen, 237
00:13:44,110 --> 00:13:49,250
I was a total disaster. 238
00:13:49,250 --> 00:13:51,290
If you take a harp, 239
00:13:51,290 --> 00:13:54,520
it is a way like a piano except there is no hammer which 240
00:13:54,520 --> 00:13:56,520
you pluck the string. 241
00:13:56,520 --> 00:13:59,500
And now there is something very special about the harp. 242
00:13:59,500 --> 00:14:02,220
You can decide where you pluck the string 243
00:14:02,220 --> 00:14:06,710
and that makes the difference in the percentage of higher 244
00:14:06,710 --> 00:14:09,430
harmonics and which high harmonic you excite. 245
00:14:09,430 --> 00:14:11,750
We will deal with that in 8.03 246
00:14:11,750 --> 00:14:13,660
when we do Fourier analysis. 247
00:14:13,660 --> 00:14:17,060
You will see then that if you pluck a string in the middle, 248
00:14:17,060 --> 00:14:19,660
that you get a different series of higher harmonics. 249
00:14:19,660 --> 00:14:21,100
Then when you pluck it, 250
00:14:21,100 --> 00:14:24,510
say a certain distance ten or twenty centimeters from the end. 251
00:14:24,510 --> 00:14:26,120
So very intresting part. 252
00:14:26,120 --> 00:14:29,410
In fact, piano is designed in such a way that the hammer 253
00:14:29,410 --> 00:14:34,160
hits the string about one-seventh of its length from one end, 254
00:14:34,160 --> 00:14:37,380
that is done to suppress the seventh harmonic. 255
00:14:37,380 --> 00:14:40,610
Know why the seventh hamornic has to be 256
00:14:40,610 --> 00:14:44,570
depressed that is a up-to-you to decide, 257
00:14:44,570 --> 00:14:46,200
maybe we don't like seventh harmonic. 258
00:14:46,200 --> 00:14:46,850
I don't know, 259
00:14:46,850 --> 00:14:48,060
It beats me but in many case, 260
00:14:48,060 --> 00:14:55,240
it's purposely done to suppress the seventh harmonic. 261
00:14:55,240 --> 00:14:58,220
There is a musical instrument that has only one string. 262
00:14:58,220 --> 00:15:00,120
One was designed by my daughter when she 263
00:15:00,120 --> 00:15:01,500
was in a nursery school. 264
00:15:01,500 --> 00:15:04,530
That's a long time ago and I have it here. 265
00:15:04,530 --> 00:15:08,110
I'm very fond of it. I've demonstrated it many times since it cause 266
00:15:08,110 --> 00:15:12,920
a washed tub base, I think. 267
00:15:12,920 --> 00:15:15,830
so you see here the one string, 268
00:15:15,830 --> 00:15:18,850
and here you see here then this surface, 269
00:15:18,850 --> 00:15:21,840
that is necessary to make you hear the string. 270
00:15:21,840 --> 00:15:26,590
This case is it a, I think, a box from KFC, 271
00:15:26,590 --> 00:15:30,300
or something like that. 272
00:15:30,300 --> 00:15:32,100
So I need three hands to play this, 273
00:15:32,100 --> 00:15:33,780
so the only thing I can do now, 274
00:15:33,780 --> 00:15:35,170
I can't change μ. 275
00:15:35,170 --> 00:15:36,270
This is a given, 276
00:15:36,270 --> 00:15:38,310
I can't change the length that a given, 277
00:15:38,310 --> 00:15:41,030
so what is the only thing I can do? 278
00:15:41,030 --> 00:15:42,250
I can change the tension. 279
00:15:42,250 --> 00:15:43,950
And that's the way you play it. 280
00:15:43,950 --> 00:15:45,440
And for whether I need three hands, 281
00:15:45,440 --> 00:15:48,410
but I will try to do this with my mouth. 282
00:15:48,410 --> 00:15:50,660
And then you listen when I increase the tension, 283
00:15:50,660 --> 00:15:52,570
you will hear the frequency goes up. 284
00:15:52,570 --> 00:15:53,980
When I decrease the tension, 285
00:15:53,980 --> 00:15:56,850
it goes down. 286
00:16:09,290 --> 00:16:10,240
You could hear it, right? 287
00:16:10,240 --> 00:16:12,150
Clearly different in frequencies. 288
00:16:16,830 --> 00:16:17,660
By Pythagoras, 289
00:16:17,660 --> 00:16:23,430
who lived in the sixth century B.C. discovered that musical modes are 290
00:16:23,430 --> 00:16:26,190
very pleasing when the length of the 291
00:16:26,190 --> 00:16:28,810
strings come in simple ratio, 292
00:16:28,810 --> 00:16:32,030
just quite remarkble when you think of that. 293
00:16:32,030 --> 00:16:34,830
Two to one gives you an octave, 294
00:16:34,830 --> 00:16:37,010
three to two gives you a fifth and 295
00:16:37,010 --> 00:16:39,900
four to three gives you a fourth. 296
00:16:39,900 --> 00:16:43,080
And the evolutional western music is based on that. 297
00:16:43,080 --> 00:16:45,290
When you take a piano, 298
00:16:45,290 --> 00:16:47,320
the piano has the octave, 299
00:16:47,320 --> 00:16:48,510
one to two. 300
00:16:48,510 --> 00:16:50,350
It has the fourth, 301
00:16:50,350 --> 00:16:50,880
four to three. 302
00:16:50,880 --> 00:16:51,510
And it has the fifth, 303
00:16:51,510 --> 00:16:53,590
three to two. 304
00:16:53,590 --> 00:16:56,080
And somehow these are very pleasant intervals 305
00:16:56,080 --> 00:16:57,720
when you play them in combination for 306
00:16:57,720 --> 00:16:59,180
our western ears, 307
00:16:59,180 --> 00:17:04,640
doesn't mean that is also true for other cultures. 308
00:17:04,640 --> 00:17:07,080
The ancient Greek astronomers, 309
00:17:07,080 --> 00:17:10,780
even all the way up to Capler in the seventeenth century, 310
00:17:10,780 --> 00:17:14,360
believe that the musical instruments could also 311
00:17:14,360 --> 00:17:17,210
explain orbits of planets. 312
00:17:17,210 --> 00:17:22,650
And this was known as the music of the spheres. 313
00:17:22,650 --> 00:17:25,060
It was believed that the movement of the planet 314
00:17:25,060 --> 00:17:27,020
produces music, 315
00:17:27,020 --> 00:17:29,700
but our ears were just not sensitive enough 316
00:17:29,700 --> 00:17:32,210
to be able to hear that music. 317
00:17:32,210 --> 00:17:34,320
And of course it shouldn't surprise you that all these 318
00:17:34,320 --> 00:17:36,780
was mixed up with religion. 319
00:17:36,780 --> 00:17:41,530
The fact that it was pleasing to hear a music 320
00:17:41,530 --> 00:17:49,400
that comes in simple ratios must show the hand of god, 321
00:17:49,400 --> 00:17:53,460
if you wanna believe that. 322
00:17:53,460 --> 00:17:57,730
And now I want to turn towards wind instruments. 323
00:17:57,730 --> 00:17:59,780
And I am going to put the wind instruments here 324
00:17:59,780 --> 00:18:05,630
which is nothing but two length L. 325
00:18:05,630 --> 00:18:09,390
Let's start with one that is closed on both sides, 326
00:18:09,390 --> 00:18:11,980
length L. 327
00:18:11,980 --> 00:18:13,690
And even it is closed on both sides, 328
00:18:13,690 --> 00:18:18,050
then the pressure here on this side and this side 329
00:18:18,050 --> 00:18:21,600
can build up as we discussed last time so it gonna be pressure. 330
00:18:21,600 --> 00:18:25,620
Antinodes (?). 331
00:18:25,620 --> 00:18:29,760
and they are going to be nodes for the motion of the molecules. 332
00:18:29,760 --> 00:18:36,680
If I have here a sound cavity which is open on both sides. 333
00:18:36,680 --> 00:18:39,710
Then I have here a pressure node and I have here a pressure node. 334
00:18:39,710 --> 00:18:42,420
Pressure can never be higher than the ambient pressure 335
00:18:42,420 --> 00:18:44,570
because it is connected with the universe. 336
00:18:44,570 --> 00:18:45,750
When I say pressure, 337
00:18:45,750 --> 00:18:46,900
I always mean over-pressure, 338
00:18:46,900 --> 00:18:49,630
over and above one atmosphere. 339
00:18:49,630 --> 00:18:52,910
And so it's immediately clear that the solution that we 340
00:18:52,910 --> 00:18:59,420
work out here for closed-cloesed system must be exactly identical to this. 341
00:18:59,420 --> 00:19:05,240
So you do get precisely here that λn 342
00:19:05,240 --> 00:19:10,150
is again 2L devided by n. That is no difference. 343
00:19:10,150 --> 00:19:16,640
And fn is nv devided by 2L. 344
00:19:16,640 --> 00:19:20,990
But of course the enormous difference is that the 345
00:19:20,990 --> 00:19:24,530
v is got given that is the speed of sounds in air, 346
00:19:24,530 --> 00:19:26,140
the air column, 347
00:19:26,140 --> 00:19:27,770
begins to oscillate. 348
00:19:27,770 --> 00:19:32,030
And so v now is approximately 340 meters 349
00:19:32,030 --> 00:19:34,600
per second which is nonnegotiable. 350
00:19:34,600 --> 00:19:37,180
So there is no way you can manipulate 351
00:19:37,180 --> 00:19:45,060
μ and T to change the speed of propagation. 352
00:19:45,060 --> 00:19:49,080
The speed of sound in a gas, 353
00:19:49,080 --> 00:19:51,560
something that I really wouldn't want you to remember, 354
00:19:51,560 --> 00:19:54,420
I will return to that at the end of my lecture is 355
00:19:54,420 --> 00:19:58,160
given by this equation which you may forget 356
00:19:58,160 --> 00:19:59,390
this part I'm concernd(see the blackboard). 357
00:19:59,390 --> 00:20:05,170
R is the gas constant.T is the temeprature of the gas in degrees kelvin? 358
00:20:05,170 --> 00:20:12,350
And γ, if any of you remember that from 8.01 is the ratio of the specific heat at constant pressure 359
00:20:12,350 --> 00:20:14,960
divided by the specific heat at constant volume. 360
00:20:14,960 --> 00:20:17,290
But if you never had that that's fine, too. 361
00:20:17,290 --> 00:20:20,410
Just take my work for it. I will give you some numbers for γ later. 362
00:20:20,410 --> 00:20:22,590
And then M is the molecular weight. 363
00:20:22,590 --> 00:20:27,910
This is the speed of sound in a gas. 364
00:20:27,910 --> 00:20:31,160
So it's given for air. There is nothing you can do about it. 365
00:20:31,160 --> 00:20:37,790
Room temperature is given. Changes with temperature which is interesting. 366
00:20:37,790 --> 00:20:44,620
So the way you get the system going you must somehow blow air path. Maybe in this direction or so. 367
00:20:44,620 --> 00:20:48,100
And then the column starts to excite. It's very hard to see why that happens 368
00:20:48,100 --> 00:20:54,970
but then the column gets into normal modes and you may get a whole collection of various normal modes, 369
00:20:54,970 --> 00:20:58,830
superposition of many normal modes. 370
00:20:58,830 --> 00:21:07,840
Now there is in the case of some cavities what is very easy to make a system which is close at one end 371
00:21:07,840 --> 00:21:10,360
and which is open at the other. 372
00:21:10,360 --> 00:21:11,880
That is very easy. 373
00:21:11,880 --> 00:21:17,220
Which you cannot do here, you can do that here. 374
00:21:17,220 --> 00:21:22,390
And so therefore in this case that one side of the cavity is close and the other one is open. 375
00:21:22,390 --> 00:21:27,330
There are musical instruments clarinet comes very close to be almost closed at one side 376
00:21:27,330 --> 00:21:31,390
and open at the other. But there are many musical instruments which are open on both sides. 377
00:21:31,390 --> 00:21:39,260
So then you will have here that (see the blackboard). 378
00:21:39,260 --> 00:21:49,420
Then you have indeed this case which will dismiss for string instruments that divided by 4L. 379
00:21:49,420 --> 00:21:54,050
And the easiest way to demonstrate that to you to take my pen. 380
00:21:54,050 --> 00:21:56,640
You see the cover of my pen. 381
00:21:56,640 --> 00:21:58,390
It is close from this side, believe me, 382
00:21:58,390 --> 00:22:03,870
and it's open here and it is about 3cm long. 383
00:22:03,870 --> 00:22:07,130
You may dislike the frequency. It's a very high bit frequency. 384
00:22:07,130 --> 00:22:14,330
And maybe a cocktail of more than one mode. 385
00:22:14,330 --> 00:22:17,950
That is a musical instrument. Not the best, but it is a musical instrument. 386
00:22:17,950 --> 00:22:23,090
Closed and open on one end and the other. 387
00:22:23,090 --> 00:22:29,550
So now it is important that we get some feeling for the frequencies 388
00:22:29,550 --> 00:22:32,870
that you can produce with the varies of wave instruments. 389
00:22:32,870 --> 00:22:36,350
And so here I have list it for you the length L 390
00:22:36,350 --> 00:22:38,850
and this is then the open-open system, 391
00:22:38,850 --> 00:22:41,210
of course it is the same for close-close system. 392
00:22:41,210 --> 00:22:44,490
But the close-close system does not make a very nice musical instrument 393
00:22:44,490 --> 00:22:46,010
because the sound is not coming out. 394
00:22:46,010 --> 00:22:47,840
So that's not the idea. 395
00:22:47,840 --> 00:22:50,700
So therefore it's open-open or it's closed-open. 396
00:22:50,700 --> 00:22:55,900
And you see here the length and of course the speed of sound is given so I can't change that. 397
00:22:55,900 --> 00:23:01,170
And this is then the fudamental the first harmonic covering the entire range of your hearing. 398
00:23:01,170 --> 00:23:06,250
All the way from 17 Hz, so you will take 10m long tube, 399
00:23:06,250 --> 00:23:11,700
open on both sides to get in the fundamental the 17 Hz. 400
00:23:11,700 --> 00:23:18,430
And for a closed-open system that would then be easier 401
00:23:18,430 --> 00:23:22,570
so you could get a way with half the length you get the same. 402
00:23:22,570 --> 00:23:30,160
You get half the frequency. That's basicly what a closed-open system does. 403
00:23:30,160 --> 00:23:38,430
And so we will keep that on so that we can understand when we hear the various frequencies, 404
00:23:38,430 --> 00:23:42,430
why the frequencies are as high or as low as there. 405
00:23:42,430 --> 00:23:53,200
Now here we have a tuning fork which is 256 Hz which is mounted on a sound cavity 406
00:23:53,200 --> 00:23:57,080
which is closed on one side and open on the other. 407
00:23:57,080 --> 00:24:02,080
And that is done in order to get perfect matching between the resonance frequency 408
00:24:02,080 --> 00:24:07,210
the fundamental of the box and the 256 Hz. 409
00:24:07,210 --> 00:24:12,270
You can do that of course if you only interested in one particular frequency. 410
00:24:12,270 --> 00:24:21,330
So for this case then you will have that the frequency f is the velocity. 411
00:24:21,330 --> 00:24:24,070
So we go to this case now. 412
00:24:24,070 --> 00:24:27,710
To the case of this equation. 413
00:24:27,710 --> 00:24:42,230
So the frequency this is the first harmonic now is (see the black board) 414
00:24:42,230 --> 00:24:46,930
And then L comes out to be about 33cm. 415
00:24:46,930 --> 00:24:54,540
And indeed if you measure the length of this you will find that is roughly 33cm. 416
00:24:54,540 --> 00:24:56,800
And so now you have the case where you have perfect matching. 417
00:24:56,800 --> 00:24:59,270
So when I hit this tuning fork 418
00:24:59,270 --> 00:25:03,820
then the box starts to love to oscillate exactly at that frequency. 419
00:25:03,820 --> 00:25:09,750
So you get very a large sound to eradiate the energy very quickly. 420
00:25:09,750 --> 00:25:16,830
You do see often tuning forks which are mounted instead this way, 421
00:25:16,830 --> 00:25:21,670
you can also have the box like this. Open and open on both sides. 422
00:25:21,670 --> 00:25:23,540
So that has to be twice as long. 423
00:25:23,540 --> 00:25:28,180
So for very high frequency tuning forks you often see it open-open. 424
00:25:28,180 --> 00:25:31,370
If we have to do it for this, it would have to be twice as long 425
00:25:31,370 --> 00:25:36,000
and that is just unpratical and not necessary of course. 426
00:25:36,000 --> 00:25:41,450
Now with musicl instruments you produce an infinite number of tones 427
00:25:41,450 --> 00:25:45,560
so that is no way that you can of course design your sounding boards 428
00:25:45,560 --> 00:25:48,110
that it resonate with every single frequency. 429
00:25:48,110 --> 00:25:52,680
And so this is where the secrecy of the manufacture comes in. 430
00:25:52,680 --> 00:25:55,140
And they are not going to tell you how they do that 431
00:25:55,140 --> 00:26:01,660
and therefore some instruments are better than others and you pay for that. 432
00:26:01,660 --> 00:26:08,930
If you have a barrel filled with liquid. 433
00:26:08,930 --> 00:26:12,940
I remember that in France they did this technique that 434
00:26:12,940 --> 00:26:17,090
I am telling you about the wine was up to here say and they want to know, 435
00:26:17,090 --> 00:26:21,250
they couldn't look into the barrel, they wanted to know where the level of the wine was. 436
00:26:21,250 --> 00:26:27,020
They would knock on this, and the sound here will be very different from the sound here 437
00:26:27,020 --> 00:26:32,300
because here is air and here is liquids. So it's obvious that where you have liquid 438
00:26:32,300 --> 00:26:37,240
that the resonances are very different from the resonances here. 439
00:26:37,240 --> 00:26:41,420
And so that's one way that you can tell what of the level is of the wine. 440
00:26:41,420 --> 00:26:45,450
When you have a cold which I happen to have today. 441
00:26:45,450 --> 00:26:49,320
I remember as a kid I would go to a doctor and he would ask me to inhale 442
00:26:49,320 --> 00:26:54,770
and then he will knock on my chest, and then I will exhale and inhale and knock on my chest 443
00:26:54,770 --> 00:26:59,600
and then he will be able to tell whether there was fluid in my lungs or not. 444
00:26:59,600 --> 00:27:04,340
I don't know how sensitive that is, it's not my feel. But that's the way it was done 445
00:27:04,340 --> 00:27:06,130
and maybe you have expierenced the same thing 446
00:27:06,130 --> 00:27:11,930
and sometimes also I don't know why you knock on your back even, you know. Fine. 447
00:27:11,930 --> 00:27:17,330
Now I have developed, in fact, I can even say invented a method 448
00:27:17,330 --> 00:27:20,740
to test for the presence of the brains. 449
00:27:20,740 --> 00:27:33,190
And the way I do that is that I strike the tuning fork and put the tuning fork on someone's head. 450
00:27:33,190 --> 00:27:35,820
And you can imagine if it's empty here, 451
00:27:35,820 --> 00:27:39,890
then you get the same effect you have with the wine barrel. 452
00:27:39,890 --> 00:27:43,050
And then you hear a very clear sound. 453
00:27:43,050 --> 00:27:48,330
But if there is brain here, like the liquids, you hear nothing. 454
00:27:48,330 --> 00:27:57,620
And that's I have pattened that so you try that at home but I can demonstrate that to you. 455
00:27:57,620 --> 00:28:06,660
You hear much? Oh.... You hear much? 456
00:28:06,660 --> 00:28:11,220
Maybe I shouldn't be lecturing 8.03 then. 457
00:28:11,220 --> 00:28:14,890
Now of course in my case I think I pass the test for the reason. 458
00:28:14,890 --> 00:28:19,130
It is not so clear of course that all students would pass that test. 459
00:28:19,130 --> 00:28:24,900
Now I am wondering whether that anyone has the courage that I may try that. 460
00:28:24,900 --> 00:28:32,540
Any one of you? You're afraid, right? You are worry that it will all come out. 461
00:28:32,540 --> 00:28:42,480
You mind? You don't mind. You are a strong man. 462
00:28:42,480 --> 00:28:46,060
You have to be quiet otherwise you can't tell the difference. 463
00:28:56,530 --> 00:29:05,040
I say no more. I think it's better that I teach 8.03 then. 464
00:29:09,720 --> 00:29:17,200
So when you design a wooden instruments the only thing you have to play with is L. 465
00:29:17,200 --> 00:29:21,280
Because T is no longer negotiable. 466
00:29:21,280 --> 00:29:25,190
And so with organ pipes when you go to churchs and you see organ pipes. 467
00:29:25,190 --> 00:29:27,660
You see a whole zoo of these organ pipes, 468
00:29:27,660 --> 00:29:34,270
open-open and closes-open and for every fudamental you want to excite you need one pipe. 469
00:29:34,270 --> 00:29:41,610
So it's a huge number of pipes. It's in the way like piano. 470
00:29:41,610 --> 00:29:47,140
If you take a flute, then you make it longer and shorter 471
00:29:47,140 --> 00:29:52,930
simply by drilling holes in it. And if you hold your hands on both holes, 472
00:29:52,930 --> 00:29:57,890
then this is the length of the flute which gives you then a lower frequency. 473
00:29:57,890 --> 00:30:02,230
Then when you take one hand off because now it's shorter. 474
00:30:02,230 --> 00:30:04,630
So this is connected with the universe. 475
00:30:04,630 --> 00:30:08,960
So here no pressure can build up, so this becomes a pressure node. 476
00:30:08,960 --> 00:30:10,060
So it's shorter. 477
00:30:10,060 --> 00:30:14,030
And if you take this one off, it's even shorter, and so the pitch will go even up. 478
00:30:14,030 --> 00:30:18,460
That's a basic idea behind a flute. And I can demonstrate that to you. 479
00:30:23,860 --> 00:30:25,350
You hear the pitch go down? 480
00:30:40,080 --> 00:30:46,210
I have here a flute-like instrument which is open on this side 481
00:30:46,210 --> 00:30:50,080
and it's also open here where we pass the air by. 482
00:30:50,080 --> 00:30:53,640
So you can consider this to a very good approximation as open-open. 483
00:30:53,640 --> 00:30:59,630
It is 16.6 cm and so if you want to know what the fundamental is. 484
00:30:59,630 --> 00:31:07,190
Well then you apply this equation and equals 1 and then you get something like 1024 Hz. 485
00:31:07,190 --> 00:31:12,980
But if you make it close at one ends and you apply this equation you will get half that. 486
00:31:12,980 --> 00:31:15,620
So you only get 512 Hz. 487
00:31:15,620 --> 00:31:22,440
The big difference fact of 2. So this is then the fundamental for open-open. 488
00:31:25,360 --> 00:31:27,060
And now comes then open-closed. 489
00:31:33,900 --> 00:31:35,130
Fact of 2 difference. 490
00:31:39,150 --> 00:31:45,490
I have here a very special tube. It is open and open at both ends 491
00:31:45,490 --> 00:31:47,560
and if you don't believe me any, 492
00:31:47,560 --> 00:31:52,460
I can see you. Can you see me? Can you? Can you see me? 493
00:31:52,460 --> 00:31:55,600
It's open and open on both sides. 494
00:31:55,600 --> 00:31:59,720
And it's corrugated which of course is very important while it works so well. 495
00:31:59,720 --> 00:32:09,760
And this has a length of 77cm. And so you can calculate now using this equation. 496
00:32:09,760 --> 00:32:11,790
And equals one what the fundamental is, 497
00:32:11,790 --> 00:32:16,700
and the fundamental is about 220 Hz, first harmonic. 498
00:32:16,700 --> 00:32:21,200
And since it's open and open at both sides, the second harmonic will be 440 Hz. 499
00:32:21,200 --> 00:32:23,380
And the third harmonic 660 Hz. 500
00:32:23,380 --> 00:32:29,330
And by touring this around with a little bit flux you can get a wind flow passed here 501
00:32:29,330 --> 00:32:35,170
which only excites the lowest mode. Sometimes you hear the lowest one and the second. 502
00:32:35,170 --> 00:32:38,620
But when you tour it faster, you get higher harmonics 503
00:32:38,620 --> 00:32:40,450
and I want to demonstrate this to you. 504
00:32:40,450 --> 00:32:45,170
I will first try to excite the 220 which is the lowest mode possible 505
00:32:45,170 --> 00:32:47,860
which is the first harmonic the fundamental. 506
00:32:47,860 --> 00:32:50,750
And I will try to make it clean, just only the fundamental. 507
00:32:55,540 --> 00:33:21,050
That's it. It's about 220 Hz. 440. 660. 880. 880. 660. 440. I can't get above 880. 508
00:33:29,780 --> 00:33:34,570
There are ways that you can change the length of the wind instruments, 509
00:33:34,570 --> 00:33:41,840
one is by making holes in it. Another one is by really physically changing the length. 510
00:33:41,840 --> 00:33:45,770
And there is one instrument which is well known for that which is the trombone. 511
00:33:45,770 --> 00:33:50,430
So you actually change the... this is a system which is open 512
00:33:50,430 --> 00:33:52,100
and is close at the end in this case, 513
00:33:52,100 --> 00:33:56,070
you can see that. It's like a piston so it's closed. 514
00:33:56,070 --> 00:34:02,320
And so now by changing the length of the cavity. You can change the fundamental. 515
00:34:02,320 --> 00:34:03,480
So we get it this way. 516
00:34:30,890 --> 00:34:37,690
We reconize instruments by the cocktail of the harmonics that they generate. 517
00:34:37,690 --> 00:34:43,410
And depend it on how you excite it, I mentioned already the plucking of the harp, 518
00:34:43,410 --> 00:34:48,380
but also the way for instant you blow on musical instruments. 519
00:34:48,380 --> 00:34:52,520
I don't know whether any of you had ever try to play on a trumpet, 520
00:34:52,520 --> 00:34:56,090
but if I gave you a trumpet, chances are that you would get no sound out of it at all. 521
00:34:56,090 --> 00:35:00,670
You have to hold your lips in special way, you have to know how to spit in there the right way. 522
00:35:00,670 --> 00:35:03,830
It goes like... something like that. 523
00:35:03,830 --> 00:35:10,800
So that is also way that you can excite certain harmonics in relation to the fundamental. 524
00:35:10,800 --> 00:35:18,010
And that then determine the sound quality of your instrument. 525
00:35:18,010 --> 00:35:24,540
And I'd like to demonstrate this to you now in various ways that the different instruments have different sound quality, 526
00:35:24,540 --> 00:35:32,640
which comes down to is that if you ask each instrument to play for instance 440 Hz tone, 527
00:35:32,640 --> 00:35:40,170
you will see that a violin cannot just simplely produce 440, but it will automatically also the same time 528
00:35:40,170 --> 00:35:43,960
generate 880 and may that is the second harmonic and maybe higher harmonics. 529
00:35:43,960 --> 00:35:50,080
And that's different for different instruments. That's of course the idea behind the tone quality. 530
00:35:50,080 --> 00:35:54,810
And the way that we are going to demonstrate that to you is as follows. 531
00:35:54,810 --> 00:36:06,190
We have here a microphone and I will first make you listen to a tuning fork. 532
00:36:06,190 --> 00:36:10,730
For instance, 440 Hz which will give you then the signal. 533
00:36:10,730 --> 00:36:15,990
Time and the amplitude of the membrane of the microphone. 534
00:36:15,990 --> 00:36:23,760
If however an instrument were to generate 440 in addition higher harmonic, you will get the sum of this signal 535
00:36:23,760 --> 00:36:25,700
and of course the higher harmonics. 536
00:36:25,700 --> 00:36:32,940
So you will see no longer a sinusoid but you will see a couple of sinusoid, the higher harmonics. 537
00:36:32,940 --> 00:36:40,620
So let me now first show you the 440 Hz. Here is the microphone. 538
00:36:43,920 --> 00:36:49,630
Boring, just one frequency. Nothing rich about it. 256. 539
00:36:53,930 --> 00:36:59,450
No indication for any higher harmonics, that's the way that tuning forks are designed. 540
00:36:59,450 --> 00:37:09,610
If I take this flute. Of course I can tell only the fundamental, no higher harmonics. 541
00:37:09,610 --> 00:37:16,280
Now maybe if you blow in a very special way maybe I can excite higher harmonics. 542
00:37:16,280 --> 00:37:21,730
But this is now.... Oh, I want to show you the 4000 Hz so that at least you can easily hear. 543
00:37:21,730 --> 00:37:24,260
This is 4000 Hz. 544
00:37:29,350 --> 00:37:32,950
All right? So you get the idea so you know now what you going to see 545
00:37:32,950 --> 00:37:36,040
but you don't know yet what you are going to hear, neither do I. 546
00:37:36,040 --> 00:37:40,840
We have six students who are very brave. I would like all of them to come down now. 547
00:37:40,840 --> 00:37:43,150
And they are going to demonstrate the musical instruments. 548
00:37:43,150 --> 00:37:44,750
So all of you come down, please. 549
00:37:48,910 --> 00:37:52,910
Yes, you will get your instruments there. 550
00:37:52,910 --> 00:37:55,670
And just come here to find or here. 551
00:38:01,460 --> 00:38:07,040
All right? Where is the violin? Where is the violin. 552
00:38:09,940 --> 00:38:12,010
Yeah, Oh, boy. Oh, boy. 553
00:38:16,270 --> 00:38:23,390
The first person who is going to demonstrate the violin is going to be Mark Avaro. 554
00:38:23,390 --> 00:38:30,740
And I am going to ask Mark first to only produce what he think that is 440 Hz. 555
00:38:30,740 --> 00:38:37,140
Now we have for you a special chair. Er... we will bring the chair very shortly. 556
00:38:37,140 --> 00:38:42,780
So let me remind you then of the 440. This is 440. 557
00:38:49,060 --> 00:38:50,940
Come a little closer and produce 440. 558
00:38:58,100 --> 00:39:01,880
Now look, did you see that? You could really see the 440 in there. 559
00:39:01,880 --> 00:39:06,560
It was the same spacing as my tuning fork. But there are many higher harmonics there. 560
00:39:06,560 --> 00:39:11,430
Show it once more. And they then give you the all these rails. 561
00:39:16,910 --> 00:39:26,650
You see? Oh. Now the audiance is yours. And now play... 562
00:39:27,520 --> 00:39:30,000
Give you 20 or 30 seconds anything you want, anything you love. 563
00:39:30,070 --> 00:39:30,590
Go ahead. 564
00:39:59,740 --> 00:40:01,280
You are fantastic. 565
00:40:09,670 --> 00:40:11,420
Is Sharon here? 566
00:40:11,420 --> 00:40:12,500
Sharon Tiu, Ah. 567
00:40:12,500 --> 00:40:15,830
So Sherren is going to demonstrate to us the flute 568
00:40:15,830 --> 00:40:17,950
and maybe you can show it to the class. 569
00:40:17,950 --> 00:40:22,020
See her flute has more holes than mine. 570
00:40:22,020 --> 00:40:23,610
I only have two. 571
00:40:23,610 --> 00:40:28,080
She has quite a few more and she opens and closes them with valves. 572
00:40:28,080 --> 00:40:30,900
Sharon, you may not be able to exactly get a 440 with this instrument 573
00:40:30,900 --> 00:40:33,160
but that's okay. 574
00:40:33,160 --> 00:40:35,920
Come close and show with your 440 575
00:40:43,800 --> 00:40:44,240
Excellent. 576
00:40:44,240 --> 00:40:46,180
If you see you could really see the 440, 577
00:40:46,180 --> 00:40:47,800
but you can see more than that. 578
00:40:47,800 --> 00:40:50,710
Seperates from the violin of course. 579
00:40:50,710 --> 00:40:51,920
Your audience is yours. 580
00:40:55,100 --> 00:40:56,490
Make us happy. 581
00:41:18,210 --> 00:41:19,070
Terrific! 582
00:41:26,210 --> 00:41:29,300
Now we have a very special guest. 583
00:41:29,300 --> 00:41:40,810
Which is a Shanna Jean who was so kind to go to the trouble of bringing her cello. 584
00:41:40,810 --> 00:41:49,390
Now you think Shanna that you can go close to 440. 585
00:41:49,390 --> 00:41:51,950
Try that? 586
00:41:51,950 --> 00:41:54,830
And if you can't do it just in the fundemental you may have to tell us wether you 587
00:41:54,830 --> 00:41:57,700
have to shorten the string with your finger. 588
00:41:57,700 --> 00:41:58,900
You do have to do that? 589
00:42:00,600 --> 00:42:01,330
Go ahead. 590
00:42:05,400 --> 00:42:07,930
Try once more, I can see the underline 440. 591
00:42:12,570 --> 00:42:14,950
And did you, you shortened the string. 592
00:42:14,950 --> 00:42:15,590
No. 593
00:42:15,590 --> 00:42:16,780
Or it was no finger on the string. 594
00:42:16,780 --> 00:42:17,180
No. 595
00:42:17,180 --> 00:42:18,650
So it is the fundemental of the string. 596
00:42:18,650 --> 00:42:19,460
Yes. 597
00:42:19,460 --> 00:42:20,600
The middle A of the piano. 598
00:42:20,600 --> 00:42:20,990
Yes. 599
00:42:20,990 --> 00:42:21,870
Show with yours. 600
00:42:21,870 --> 00:42:23,750
Oh I don't practise anything. PAGE2
Last Modified 3/4/06 6:37 AM
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