00:01
Observing from the figure 15 .20, we can see that the wave moving to the left is actually inverted and reflected both.
00:10
When the wave is reflected, that means that the wave will be moving in the opposite direction of the positive direction, and while moving to the left, it is moving in the negative horizontal direction.
00:25
Also when the wave is reflected in this given case it also means that it's its whole functional parity will be inverted as well so first reflection means the wave is moving out to the different opposite direction and since the wave is moving to the negative x direction this implies that the function will get a negative sign no matter what the function is this is a form of representation for the wave function no matter what this way function is it will now get negative sign now also since the very small to the left and it is obtained from the wave moving to the right by rotation or by degrees by radian radiance the coordinate and the function will have their signs changed.
01:36
So this is the explanation for the question in the part a of this problem.
01:41
For the part b in this problem, we're actually asked to show that, no, it will always, when we have two wave functions at the point o, their total wave function will always equal to zero independently from the type of the wave function.
02:02
And to prove this we'll say that the first wave function can be represented as y1 from x and t and also also we need to also we need to express the second function which is the function of the reflected wave now this is a function that must have a different sign so we'll say that this y2 of x and t is actually y of minus x if this function is equal to y of x.
02:50
So by this condition, the linear combination of these functions, which is y1 of x and t, plus y2 of x and t, it's the same thing as if we said that we're actually adding two functions, so that the combination function will just name it.
03:19
With y.
03:21
The function combination is the combination of two functions where one function is fx.
03:28
It's some arbitrary function.
03:30
It can be any kind of function as long as it's continuous and depending on these variables and it's applicable to the problem of maze.
03:42
And it is then added with the same function, but the sign of the function is negative, it's opposite of this function.
03:57
So minus f effects.
04:02
For any f, this kind of addition will be zero.
04:07
And to be more general, we can say that, in fact, it will be f, for example, of zero.
04:16
That's the point o, minus f of minus zero.
04:21
We need to take into account that in the argument, the sign changes well since both the phase and the direction change in for any x for any for any f and for x equal zero this this relation this subtraction will be equal to zero and this proves the part b of this problem for the part c we need to actually explain that this rather do waves that combine so and we see the slope the 0 is also always 0...