00:02
Here we're going to be looking at standing waves on a string.
00:07
And the experiment you can do with such a system is to oscillate usually at a fixed frequency, although you can get oscillators that can vary.
00:20
And you're trying to excite standing waves on the string.
00:26
And you will find that only certain patterns can be produced over the length of the string and it takes just the right amount of tension in the string, which you usually create by hanging a mass on the end of the string over a pulley.
00:46
So it's keeping that string under tension.
00:50
So to understand how this is working, there are two things to work with.
00:54
One is the usual speed of a wave is a product of its frequency times its wavelength.
01:03
And here our frequency is the frequency of the oscillator, which we will assume to be 60 hertz.
01:11
So that is fixed.
01:14
What governs the speed of the wave? this is usually a specific relationship that depends on what type of wave it is and what material it's going through.
01:26
For a wave on a string, that specific relationship is that this space.
01:33
Is the square root of the tension in the string divided by its mass per unit length.
01:43
So we have tension and we have mass per unit length.
01:58
Now we're going to assume the same string throughout the experiment, so the mass per unit length is not going to vary, at least not in this experiment.
02:12
You could do this in real life.
02:15
You could swap out different strings.
02:19
And that mass is small enough that we can still assume that tension gets transmitted without diminishment throughout the string.
02:30
We're going to use a string of length 1 .5 meters so we can see that the mass is not even in the gram range.
02:42
So the tension is being created by the weight being hung down.
02:50
So our tension is equal to mg.
02:54
And that has to be just exact to excite the right standing wave on the string.
03:01
But what we can see happening is as the tension is increased, the speed will increase and the wavelength will increase.
03:12
So as an example of working with this, let's look at the standing wave patterns that can be created.
03:26
As shown above, you have to worry about what happens at the end, and we are going to assume what are called nodes on both ends.
03:42
If that is the case, then what you have to create on that string is a pattern that has full loops in it as the one that's shown has two loops.
03:55
But each loop, and we'll call those antinodes, represents the middle center of one half of a wavelength.
04:14
Okay, so recall what a wavelength looks like.
04:18
The wave repeats.
04:20
Now, usually what's happening is the oscillations are so quick that you just see kind of a blur, and you see these loopy type structures.
04:28
But each one is occupying a space of one -half of a wavelength.
04:36
So by adjusting the weight, you will find all of a sudden a pattern arise.
04:44
You can count the loops, and therefore you can basically see the wavelength that's present, and then see if it matches the...
05:00
Tension is on the bully.
05:05
So let's do some cases...