00:01
So here i'm going to be looking at a waveform on a string.
00:07
The way i'm going to cast it to begin with is as a sine wave.
00:14
So i don't have to worry too much about phase.
00:17
But we'll be looking at some clues from the graph to figure out what the parameters are in the wave.
00:28
So the first thing to worry about is we are told that the wave is moving to the right.
00:34
And what i know is i can put an opposite sign between my space and my time part.
00:43
So notice that i have a minus sign in between them, and that represents a wave moving to the right.
00:51
If they both had the same sign, either both positive or both negative, we would be representing a wave moving to the left.
01:00
I'll say how you can verify this with some graphical tools.
01:06
But there's typically also a phase that's added in there.
01:11
And i'm going to start with a sign function because i notice at x equals zero and t equals zero, the pink curve looks like a sine wave.
01:34
Okay, and we'll say a few words about that later.
01:38
But what we are putting in is a is the amplitude, and i can read that off the graph.
01:46
That is the maximum swing of the wave.
01:51
And i can read that very nicely.
01:54
That amplitude is basically 4 millimeters.
02:02
I'll just call it 4 when i write the function.
02:07
The other things that we need to put in are k.
02:12
K is related to the wavelength 2 pi over lambda in radiance per meter.
02:19
And what i see is i cannot see a wavelength on this graph.
02:23
So we want to take a look at the x -axis is time.
02:29
But what we can read off of that is omega is 2 pi over the period.
02:35
A period is a time quantity.
02:39
So i'm going to pick off one full period.
02:43
It's a time between one maximum and the next.
02:47
It's usually the easiest thing to read.
02:50
So the period in this case is simply 0 .05 minus 0 .01 .1 .5 minus 0 .01 seconds.
03:03
So it's the time that's elapsed between one peak and the next.
03:13
Okay, so we can figure out omega then.
03:16
That turns out to be 50 pi radians per second.
03:28
We'll verify that a little bit.
03:30
Now, in order to get k, the other parameter that's usually important is the wave speed, which is omega over k.
03:38
They give us enough information to determine the speed.
03:44
What i notice is with the data given is that the peak has moved over by a certain amount.
04:01
Okay, yeah, it's getting a little confusing already.
04:05
But if you take a look at the blue curve and the pink curve, what we see is the peak from the pink curve has moved by, 0 .090 meters.
04:28
So that's the x on the blue curve in how many seconds, basically.
04:34
0 .035, roughly, minus 0 .01 seconds.
04:45
Now, how do you know that's the peak associated with that pink peak? they give some information that the wavelength is within the 0 .0 meters.
04:57
So we're feeling pretty good that we have haven't lost a peak movement at a shorter time.
05:06
So we're going to go ahead and say that the speed is 0 .09 meters divided by 0 .025 seconds.
05:23
Again, we can verify that this could reproduce these graphs, and that is 3 .6 meters per second.
05:32
So once we find that, we can plug into our what's called dispersion relationship for the speed and solve for the k.
05:47
Now let's do this a little bit differently.
05:50
That's kind of awkward.
05:52
So k equals omega over v equals 50 pi over 3 .6 and that should be in radiance per meter.
06:10
That turns out to be about 0 .14.
06:16
1.
06:18
Yeah, 0 .14.
06:30
No, 13 .9...