00:01
So i'll start off by reviewing the standing waves on a string that is clamped at both ends.
00:07
So a reminder that a standing wave is a pattern of nodes and antinodes that are created when the wave reflects from a boundary and combines with the incoming wave.
00:26
So if the string is clamped at both ends, every time the wave, runs into the end of the string, it will reflect back onto the string and combined with the incident wave.
00:39
In terms of the patterns that get formed on such a system, so the endpoints are clamped, and that means you have so -called nodes at the endpoints, which means that the string is not moving there.
00:56
It oscillates up and down in between, sometimes.
01:02
Maximum, sometimes the string appears to be leveled out.
01:09
And of course, it depends what part of the oscillation you're looking at, whether the string is oscillating up or oscillating down or looking level.
01:21
But in any event, the wavelength depends on which pattern you're producing.
01:27
The first pattern i have drawn here is called the first harmonic, sometimes called the fundamental as well.
01:35
And we can see that the length is equal to one half of a wavelength.
01:43
So on the entire string, there's a half a wavelength.
01:48
And for the second harmonic, there is a full wavelength.
01:56
For the third harmonic, there is one and a half wavelengths on the string, or three halves of a wavelength.
02:08
So we can actually write a relationship between the length and the wavelength as length is equal to lambda times the harmonic over two.
02:22
Okay, n is the harmonic number.
02:29
So, of course, the wavelength keep getting shorter as the harmonics go up.
02:37
Now, the other thing about a wave on a string is that there is a well -known formula for the speed of the wave.
02:47
So that's the v of the wave, is the square root of the tension in the string divided by the mass per unit length.
02:58
So t is the tension, whether that is created by hanging weights or by pegs...
