00:01
This is a question that actually requires a graphing calculator.
00:05
So i don't have a calculator to show you guys, so i would just try.
00:09
So i just try to draw this question as best as i can, but this is a question that is supposed to be done with a graph and calculator.
00:19
So we are given a couple numbers.
00:21
We are given a equals 0 .15 meter, k equals 3 .5 per meter plus or minus 1 .1.
00:33
T because this is d and in part a we chose t to be one second so this would just be 1 .8 so this is the expression you should put into your calculator but we also say we want to have at least one wavelength so it doesn't occur to try to find the wavelengths the wavelength is 2 pi over k which is pi 2 pi over 3 .5 per meter which is around 1 .8 meter.
01:11
And that is the wavelength, draw the graph, setting the x, the graphing calculator sets the x maximum to be at least 1 .8, and the amplitude we would expect to be 0 .15 and negative 0 .15.
01:42
If you have the calculator, you will see that the actual wave looks something like this.
02:01
So this is for d2, which is the wave with the plus sign that is traveling to the left.
02:12
And for the wave with the minus sign, d1, oh, this is d1.
02:16
So this is d1, which is a wave with minus sign that's traveling to the right.
02:24
And we also have d2, which is a wave with a plus sign that's traveling to the left, and that will look like something like this.
02:35
So you can see that compared to a normal sine wave, a normal sine wave who looks like this, this is roughly, it almost looked like it's shifted by around one -fourths of a wavelength.
02:58
And that is because if we inspect, if we look at this, we can see that 1 .8 is around half of x.
03:07
So that is to say by introducing this extra time of one second, it's almost equivalent to moving x to the left or right by roughly 0 .5.
03:21
And 0 .5 is roughly 1 fourth of a wavelength.
03:26
So it's like it's a normal sine wave except that it's shifted to the left or right by a little bit more than 0 .2.
03:39
One -fourth of a wave lens.
03:42
But anyway, that is part a.
03:45
And we look at part b.
03:47
The part b asks us to plot the sum of the two waves and to identify the knot and anti -not as a plot...