1
00:00:00,000 --> 00:00:00,630


2
00:00:00,630 --> 00:00:03,170
Let's say I've got a rope.

3
00:00:03,170 --> 00:00:04,580
That's my rope.

4
00:00:04,580 --> 00:00:07,220
And what I'm going to do is, I'm
going to take the left end

5
00:00:07,220 --> 00:00:08,910
of the rope, and I'm going
to jerk it up,

6
00:00:08,910 --> 00:00:10,070
and then back down.

7
00:00:10,070 --> 00:00:13,190
And we're going to talk about
what happens or what possibly

8
00:00:13,190 --> 00:00:14,460
gets formed.

9
00:00:14,460 --> 00:00:19,140
So if I take it up over here,
it's going to, obviously, take

10
00:00:19,140 --> 00:00:21,300
the string to the right
of it up with it.

11
00:00:21,300 --> 00:00:24,170
And the string is going to
look something like this.

12
00:00:24,170 --> 00:00:26,030
It's going to look something
like that.

13
00:00:26,030 --> 00:00:29,060
Now I'm going to immediately
jerk it back down.

14
00:00:29,060 --> 00:00:31,470
And as it passes, let's see what
the rope will look like

15
00:00:31,470 --> 00:00:35,160
when the left-hand point is at
its original position again.

16
00:00:35,160 --> 00:00:37,690
So the left-hand point-- I've
pulled it back down.

17
00:00:37,690 --> 00:00:41,800
But in the last time period,
this part of the rope had some

18
00:00:41,800 --> 00:00:43,320
type of an upward velocity.

19
00:00:43,320 --> 00:00:44,940
You could imagine that way.

20
00:00:44,940 --> 00:00:48,340
And even after that point, even
though this left-hand

21
00:00:48,340 --> 00:00:53,720
point starts getting pulled
down, this point right here

22
00:00:53,720 --> 00:00:55,080
still has some upward
momentum.

23
00:00:55,080 --> 00:00:57,430
So it's still going to keep
moving up, maybe at a slower

24
00:00:57,430 --> 00:00:59,710
pace because it's starting
to be tugged down by

25
00:00:59,710 --> 00:01:00,550
the rope on its left.

26
00:01:00,550 --> 00:01:02,130
So it's going to look
something like that.

27
00:01:02,130 --> 00:01:05,099
And it's going to bring the
rope to its right with it.

28
00:01:05,099 --> 00:01:08,032
So the rope will look
something like this.

29
00:01:08,032 --> 00:01:10,480
The rope might look something
like that.

30
00:01:10,480 --> 00:01:13,600
And then I'm going to take this
guy-- this was just an

31
00:01:13,600 --> 00:01:16,160
intermediate position on the
way to being pulled all the

32
00:01:16,160 --> 00:01:17,410
way down here.

33
00:01:17,410 --> 00:01:24,150


34
00:01:24,150 --> 00:01:26,560
So what's the rope going
to look like now?

35
00:01:26,560 --> 00:01:27,160
Well.

36
00:01:27,160 --> 00:01:30,820
This guy, he had some momentum
that got him there.

37
00:01:30,820 --> 00:01:33,490
But then all of that velocity
will essentially go to zero

38
00:01:33,490 --> 00:01:35,850
because he's being tugged
by the rope to the left.

39
00:01:35,850 --> 00:01:37,580
And now, he's going to
switch directions.

40
00:01:37,580 --> 00:01:40,820
And he will have gotten
here, at that point.

41
00:01:40,820 --> 00:01:45,770
The point on the line that was
here-- on the purple period of

42
00:01:45,770 --> 00:01:47,780
time-- it had some
upward momentum.

43
00:01:47,780 --> 00:01:50,000
So it's just going to keep
going, on maybe a slower pace.

44
00:01:50,000 --> 00:01:52,400
It'll be there and it will bring
the rest of the rope to

45
00:01:52,400 --> 00:01:53,290
the right of it with it.

46
00:01:53,290 --> 00:01:55,650
So now my rope is going to
look something like this.

47
00:01:55,650 --> 00:01:58,790


48
00:01:58,790 --> 00:02:01,410
And then finally, where I'm
going to jerk the rope back to

49
00:02:01,410 --> 00:02:03,710
its original position-- so this
left-hand point is going

50
00:02:03,710 --> 00:02:06,180
to be there.

51
00:02:06,180 --> 00:02:09,580
This guy, in the previous
time period,

52
00:02:09,580 --> 00:02:11,060
was moving down rapidly.

53
00:02:11,060 --> 00:02:13,840
So he might get there ready to
switch directions again.

54
00:02:13,840 --> 00:02:15,780
This guy will start
moving down.

55
00:02:15,780 --> 00:02:19,080
This guy, right here, he had
some upward momentum.

56
00:02:19,080 --> 00:02:21,590
So he's going to be up
in this position now.

57
00:02:21,590 --> 00:02:23,390
And he's going to be ready
to switch directions.

58
00:02:23,390 --> 00:02:25,540
So finally, when I've done this
whole cycle, when I've

59
00:02:25,540 --> 00:02:29,610
moved up, down and back there
again, my rope might look

60
00:02:29,610 --> 00:02:32,650
exactly like this.

61
00:02:32,650 --> 00:02:33,940
And I could let go
of the rope.

62
00:02:33,940 --> 00:02:38,210
I could just leave this little
left point right there.

63
00:02:38,210 --> 00:02:41,230
And this the lump is going to
propagate along the rope.

64
00:02:41,230 --> 00:02:42,760
Because in the next moment
of time, what's it

65
00:02:42,760 --> 00:02:44,080
going to look like?

66
00:02:44,080 --> 00:02:47,590
This guy is going to be pulled
up by this left-hand point.

67
00:02:47,590 --> 00:02:50,550
So he'll go back to his
resting position.

68
00:02:50,550 --> 00:02:53,770
This guy's being pulled down
right here by the part of the

69
00:02:53,770 --> 00:02:56,050
rope to the left of him, so he's
going to be pulled down.

70
00:02:56,050 --> 00:02:58,730
This guy's being pulled down.

71
00:02:58,730 --> 00:03:01,550
But this guy had some upward
momentum in the time period

72
00:03:01,550 --> 00:03:03,530
before, so he will
have moved up.

73
00:03:03,530 --> 00:03:06,860
And so, the very next time
period, my rope is going to

74
00:03:06,860 --> 00:03:08,110
look something like this.

75
00:03:08,110 --> 00:03:13,300


76
00:03:13,300 --> 00:03:16,600
And this disturbance in the
rope, if I do nothing else,

77
00:03:16,600 --> 00:03:19,480
and if I don't lose energy to
heat and friction and all

78
00:03:19,480 --> 00:03:22,610
that, it'll just continue
moving down the rope.

79
00:03:22,610 --> 00:03:25,890
If I look at the rope at some
future period in time, maybe

80
00:03:25,890 --> 00:03:29,410
not that far down, the rope will
look something like this.

81
00:03:29,410 --> 00:03:32,590
And if I were to keep watching
it, I'll see this disturbance.

82
00:03:32,590 --> 00:03:34,090
I keep using the word
disturbance, because there's

83
00:03:34,090 --> 00:03:37,010
really no better word
to use for it.

84
00:03:37,010 --> 00:03:40,110
I'll see this disturbance or
perturbation, or whatever you

85
00:03:40,110 --> 00:03:43,950
want to call it, moving
along the rope.

86
00:03:43,950 --> 00:03:47,700
When we think about what a wave
is, we essentially-- I

87
00:03:47,700 --> 00:03:49,620
kind of jumped the gun-- I
keep calling this is a

88
00:03:49,620 --> 00:03:51,890
disturbance, because I didn't
want to use the word, wave. I

89
00:03:51,890 --> 00:03:53,940
want to say, well what
really is a wave?

90
00:03:53,940 --> 00:03:57,890
And a wave really is just this
disturbance that's propagating

91
00:03:57,890 --> 00:03:59,190
down the rope.

92
00:03:59,190 --> 00:04:02,978
So this is a good time to
actually define a wave. A

93
00:04:02,978 --> 00:04:05,820
wave. Because once I define it,
I can start calling this a

94
00:04:05,820 --> 00:04:07,450
wave, as opposed to
a disturbance

95
00:04:07,450 --> 00:04:09,320
propagating down the rope.

96
00:04:09,320 --> 00:04:15,630
So a wave is a disturbance
propagating through space.

97
00:04:15,630 --> 00:04:24,340


98
00:04:24,340 --> 00:04:27,755
And you might see other
definitions of a wave. One of

99
00:04:27,755 --> 00:04:32,020
the most typical ones is
energy or a disturbance

100
00:04:32,020 --> 00:04:35,010
propagating energy
through a medium.

101
00:04:35,010 --> 00:04:36,420
And when they say medium,
it's what is

102
00:04:36,420 --> 00:04:37,380
the wave going through?

103
00:04:37,380 --> 00:04:42,810
So in this example, the rope
would be our medium.

104
00:04:42,810 --> 00:04:46,560
But the reason why I don't want
to use that definition of

105
00:04:46,560 --> 00:04:49,210
a wave is because in future
videos, we'll learn about

106
00:04:49,210 --> 00:04:52,920
electromagnetic waves and those
don't propagate through

107
00:04:52,920 --> 00:04:53,680
any medium.

108
00:04:53,680 --> 00:04:55,440
They propagate through
a vacuum.

109
00:04:55,440 --> 00:04:58,380
So to keep things as general as
possible, we'll just call

110
00:04:58,380 --> 00:05:01,050
it a disturbance that propagates
through space.

111
00:05:01,050 --> 00:05:02,835
And it usually transfers
energy.

112
00:05:02,835 --> 00:05:17,030


113
00:05:17,030 --> 00:05:19,590
What do I mean by transferring
energy?

114
00:05:19,590 --> 00:05:21,660
On this left hand part
of the rope, I gave a

115
00:05:21,660 --> 00:05:22,540
little energy the rope.

116
00:05:22,540 --> 00:05:25,420
I moved it up, down, and
then back again.

117
00:05:25,420 --> 00:05:28,420
And then after I did that, that
up, down, back again is

118
00:05:28,420 --> 00:05:30,780
happening successively
to every point to the

119
00:05:30,780 --> 00:05:31,750
right on the rope.

120
00:05:31,750 --> 00:05:34,570
So if I waited long enough, at
this point on the rope right

121
00:05:34,570 --> 00:05:38,810
here, it's going to move up,
down, and then back again.

122
00:05:38,810 --> 00:05:41,040
Exactly what I did over here
is going to happen to this

123
00:05:41,040 --> 00:05:41,730
point on the rope.

124
00:05:41,730 --> 00:05:43,740
And then later on, it's going to
happen to some other future

125
00:05:43,740 --> 00:05:44,620
point on the rope.

126
00:05:44,620 --> 00:05:46,720
So that energy that I originally
put on the

127
00:05:46,720 --> 00:05:48,390
left-hand side of the
rope is being

128
00:05:48,390 --> 00:05:49,830
transferred down the rope.

129
00:05:49,830 --> 00:05:54,890
If I had some type of object
here sitting on the rope,

130
00:05:54,890 --> 00:05:59,440
maybe when the wave-- when the
disturbance- passes by it,

131
00:05:59,440 --> 00:06:01,710
this thing could get flipped
into the air; it might get

132
00:06:01,710 --> 00:06:03,800
pushed into the air,
and go into a

133
00:06:03,800 --> 00:06:05,530
higher potential energy.

134
00:06:05,530 --> 00:06:08,410
So this disturbance
is transferring

135
00:06:08,410 --> 00:06:10,320
energy in this case.

136
00:06:10,320 --> 00:06:13,440
Now, what I've drawn here isn't
the only type of wave

137
00:06:13,440 --> 00:06:16,620
you can have. I mean my
definition is fairly general.

138
00:06:16,620 --> 00:06:19,660
But the definition is more
general than just what I've

139
00:06:19,660 --> 00:06:20,270
drawn here.

140
00:06:20,270 --> 00:06:28,770
For example, you could have a
sound wave. If you just look

141
00:06:28,770 --> 00:06:33,110
at all of the molecules of the
air, they have some density

142
00:06:33,110 --> 00:06:35,850
that looks something
like that.

143
00:06:35,850 --> 00:06:38,620
And now let's say I had some
type of a membrane-- maybe

144
00:06:38,620 --> 00:06:41,480
it's a speaker--
that jolts this

145
00:06:41,480 --> 00:06:42,680
left-hand side of the air.

146
00:06:42,680 --> 00:06:46,820
So it just pushes-- so let me
see if I can draw this.

147
00:06:46,820 --> 00:06:52,560
Let's say I had some type of
surface here that just really

148
00:06:52,560 --> 00:06:55,440
quickly jolts-- that just moves
it in that direction,

149
00:06:55,440 --> 00:06:56,590
and then just comes back.

150
00:06:56,590 --> 00:06:58,630
So similar to what I did
here, I go up and down.

151
00:06:58,630 --> 00:07:01,320
But instead of doing that, it
just pushes the air and then

152
00:07:01,320 --> 00:07:02,010
pushes back.

153
00:07:02,010 --> 00:07:03,440
So what's going to happen?

154
00:07:03,440 --> 00:07:06,220
Right after it pushes it, the
air molecules that it pushes

155
00:07:06,220 --> 00:07:08,940
up against are going
to jam together.

156
00:07:08,940 --> 00:07:11,120
They're going to
get compressed.

157
00:07:11,120 --> 00:07:13,330
Right here, all these air
molecules that were right on

158
00:07:13,330 --> 00:07:15,490
the surface, they're going to
get pushed next to all these

159
00:07:15,490 --> 00:07:17,550
air molecules that
are right there.

160
00:07:17,550 --> 00:07:20,760
And then when it pushes back,
or when the membrane goes

161
00:07:20,760 --> 00:07:23,280
back, you're going to have
fewer air molecules here,

162
00:07:23,280 --> 00:07:25,050
because you're going to have
a low density here.

163
00:07:25,050 --> 00:07:28,030
And then these guys, that are
all scrunched up together,

164
00:07:28,030 --> 00:07:29,800
they're going to want to get
away from each other.

165
00:07:29,800 --> 00:07:31,750
They might even run
into each other.

166
00:07:31,750 --> 00:07:34,520
And so these guys are going to
run into those guys, who are

167
00:07:34,520 --> 00:07:35,950
going to run into
the next guys.

168
00:07:35,950 --> 00:07:37,060
And so on and so forth.

169
00:07:37,060 --> 00:07:39,680
And after these guys bump into
those guys, those guys are

170
00:07:39,680 --> 00:07:41,170
going to go back to
where they were.

171
00:07:41,170 --> 00:07:43,750
So essentially, you're going
to have this disturbance

172
00:07:43,750 --> 00:07:48,950
that's going to be a set of
molecules compressing, or

173
00:07:48,950 --> 00:07:50,620
bumping into, its neighboring
molecules.

174
00:07:50,620 --> 00:07:54,360
So if you look at this at some
future period in time, all of

175
00:07:54,360 --> 00:07:57,040
a sudden, this area
might look normal.

176
00:07:57,040 --> 00:08:01,330
Let me clear it and draw it
just the way it I started.

177
00:08:01,330 --> 00:08:02,835
So this area might
look normal.

178
00:08:02,835 --> 00:08:06,620


179
00:08:06,620 --> 00:08:09,690
But that compression of the
particles might have reached

180
00:08:09,690 --> 00:08:10,940
right over here.

181
00:08:10,940 --> 00:08:15,440


182
00:08:15,440 --> 00:08:17,930
And not only that, we saw that
right after the compression,

183
00:08:17,930 --> 00:08:20,960
you usually have this area
of low pressure.

184
00:08:20,960 --> 00:08:24,450
So if I were to really draw this
wave, and actually, if

185
00:08:24,450 --> 00:08:27,210
this membrane were to keep doing
it over, and over, and

186
00:08:27,210 --> 00:08:30,340
over again-- so it kept going
forward and back, forward and

187
00:08:30,340 --> 00:08:32,520
back, or right and left, right
and left-- what you would have

188
00:08:32,520 --> 00:08:34,650
is a series of compressions.

189
00:08:34,650 --> 00:08:36,630
The air would just have a
series of compressions.

190
00:08:36,630 --> 00:08:38,120
So that's one compression.

191
00:08:38,120 --> 00:08:41,780
You'd have another compression
right there.

192
00:08:41,780 --> 00:08:44,250
Another compression
right there.

193
00:08:44,250 --> 00:08:45,700
And then, in between
the compressions

194
00:08:45,700 --> 00:08:47,780
the air is less dense.

195
00:08:47,780 --> 00:08:50,550
The air is less dense
like this.

196
00:08:50,550 --> 00:08:53,790
And what we've essentially just
generated is a sound wave

197
00:08:53,790 --> 00:08:55,570
travelling through air.

198
00:08:55,570 --> 00:09:02,060
So this right here is a sound
wave. And this type of wave,

199
00:09:02,060 --> 00:09:06,500
where the direction of the
disturbance is the same, or

200
00:09:06,500 --> 00:09:09,570
along the same axis as the
direction in which the wave is

201
00:09:09,570 --> 00:09:12,150
travelling-- the wave is
travelling in that direction--

202
00:09:12,150 --> 00:09:16,570
this is call a longitudinal
wave. So sound waves sound

203
00:09:16,570 --> 00:09:18,410
through air, they're
longitudinal waves.

204
00:09:18,410 --> 00:09:23,400


205
00:09:23,400 --> 00:09:28,090
Sometimes called a compression
wave. Same thing.

206
00:09:28,090 --> 00:09:31,720
Compression wave. Because it's
caused by compression.

207
00:09:31,720 --> 00:09:35,110
Our example of the string, this
is called a transverse

208
00:09:35,110 --> 00:09:44,100
wave. Because the disturbance,
the movement of the medium, is

209
00:09:44,100 --> 00:09:48,040
going in a direction transverse
to-- or at an axis

210
00:09:48,040 --> 00:09:50,250
that's transverse to-- the
direction of our movement.

211
00:09:50,250 --> 00:09:53,660
We're moving in that direction,
to the right.

212
00:09:53,660 --> 00:09:56,190
Actually, our wave is moving to
the right, but the actual

213
00:09:56,190 --> 00:09:58,310
medium is moving up and down.

214
00:09:58,310 --> 00:10:00,670
Our medium is moving
up and down.

215
00:10:00,670 --> 00:10:02,500
That's why this is called
transverse.

216
00:10:02,500 --> 00:10:05,160
While here the medium is moving
left and right while

217
00:10:05,160 --> 00:10:06,980
the wave moves to the right.

218
00:10:06,980 --> 00:10:08,310
So it's along the same axis.

219
00:10:08,310 --> 00:10:11,710
So we're dealing with the
compressional or longitudinal.

220
00:10:11,710 --> 00:10:14,980
Now in this first example,
I just did one cycle.

221
00:10:14,980 --> 00:10:18,280
I just jerked up, down,
and back again.

222
00:10:18,280 --> 00:10:20,510
And I created this
one disturbance.

223
00:10:20,510 --> 00:10:23,205
And we can call this, when you
just do it once, you can view

224
00:10:23,205 --> 00:10:24,455
this as a wave pulse.

225
00:10:24,455 --> 00:10:26,860


226
00:10:26,860 --> 00:10:29,710
If I kept doing that-- if I
just went up, down, back

227
00:10:29,710 --> 00:10:31,470
again, up, down, back again,
and I kept doing it

228
00:10:31,470 --> 00:10:34,760
periodically, over and over
again, then I would generate a

229
00:10:34,760 --> 00:10:37,080
periodic wave. And my
string would look

230
00:10:37,080 --> 00:10:38,330
something like this.

231
00:10:38,330 --> 00:10:43,610


232
00:10:43,610 --> 00:10:50,200
Well actually, it would look
something that right there,

233
00:10:50,200 --> 00:10:54,930
where that's the disturbance
generated from our first time

234
00:10:54,930 --> 00:10:59,600
that we moved this left-hand
part of our string.

235
00:10:59,600 --> 00:11:03,840
So this right here is
a periodic wave.

236
00:11:03,840 --> 00:11:05,790
In the next video, we're going
to talk about a lot of the

237
00:11:05,790 --> 00:11:09,800
properties of a periodic wave.
How the wavelength, and its

238
00:11:09,800 --> 00:11:12,330
frequency, and its period relate
to its velocity, and

239
00:11:12,330 --> 00:11:13,100
all of that.

240
00:11:13,100 --> 00:11:14,870
But I'll leave that alone
in this video.

241
00:11:14,870 --> 00:11:17,910
But I just wanted you to
appreciate what I think is a

242
00:11:17,910 --> 00:11:20,420
concept that we use
in everyday life.

243
00:11:20,420 --> 00:11:22,290
So it's a wave, it's a sound
wave, and all that.

244
00:11:22,290 --> 00:11:24,610
But it's a fairly abstract
notion where we talk about a

245
00:11:24,610 --> 00:11:27,590
wave, we're really just pointing
to a disturbance

246
00:11:27,590 --> 00:11:30,980
that's moving, usually along
a medium, at least when we

247
00:11:30,980 --> 00:11:32,720
visualize it, but not always.

248
00:11:32,720 --> 00:11:34,210
But we're just pointing
to this disturbance.

249
00:11:34,210 --> 00:11:37,000
And this disturbance could take
many forms. It could be a

250
00:11:37,000 --> 00:11:39,940
transverse disturbance if we're
dealing with a string.

251
00:11:39,940 --> 00:11:44,370
It could be a disturbance in
terms of the density of air

252
00:11:44,370 --> 00:11:47,440
molecules in terms of a sound
wave. And there is a relation.

253
00:11:47,440 --> 00:11:53,120
So if you wanted to just plot
the density here by position--

254
00:11:53,120 --> 00:11:55,920
if I were to mathematically
represent this compression

255
00:11:55,920 --> 00:11:59,300
wave right here-- let's say that
this line represents just

256
00:11:59,300 --> 00:12:02,380
resting before the sound
wave hits, that's

257
00:12:02,380 --> 00:12:03,700
just your normal density.

258
00:12:03,700 --> 00:12:05,510
If we were to plot the
density it might look

259
00:12:05,510 --> 00:12:07,410
something like this.

260
00:12:07,410 --> 00:12:08,870
Over here, we have very
high density.

261
00:12:08,870 --> 00:12:10,240
Over here, we have
very low density.

262
00:12:10,240 --> 00:12:11,610
Over here, we have very
high density.

263
00:12:11,610 --> 00:12:15,930
And if you were to plot it, it
would look a lot like that

264
00:12:15,930 --> 00:12:21,090
transverse wave that I did with
the rope at the beginning

265
00:12:21,090 --> 00:12:21,950
of this video.

266
00:12:21,950 --> 00:12:23,760
And that's why they're even
grouped together.

267
00:12:23,760 --> 00:12:26,460
Because mathematically, even
though a compression wave

268
00:12:26,460 --> 00:12:29,180
looks very different, or
you might visualize or

269
00:12:29,180 --> 00:12:31,340
conceptualize it very different
than a transverse

270
00:12:31,340 --> 00:12:34,190
wave, mathematically, they're
essentially the same thing.

271
00:12:34,190 --> 00:12:35,610
You have this quantity.

272
00:12:35,610 --> 00:12:39,170
In this case, it's the density
of the air varying over time.

273
00:12:39,170 --> 00:12:43,400
In this case, it's the height,
or the position, or how much

274
00:12:43,400 --> 00:12:45,860
your displacement from your
resting position-- that's the

275
00:12:45,860 --> 00:12:50,530
quantity varying through time,
that disruption is travelling

276
00:12:50,530 --> 00:12:51,700
over the course of the medium.

277
00:12:51,700 --> 00:12:54,600
That's why we call both
of these things waves.

278
00:12:54,600 --> 00:12:56,560
Anyway, I'll let you go here.

279
00:12:56,560 --> 00:12:58,500
And in the next video, we'll
talk a little bit more of the

280
00:12:58,500 --> 00:13:01,700
properties of periodic waves.

281
00:13:01,700 --> 00:00:00,000