Superposition Proof: Understanding Angle of Sin

[Neon32]

I don't get the first part. why did he make the angle of sin equal to n pi.

 

[pixel]

A node is a location where the amplitude is zero. The sin function is zero when its argument is a multiple of π radians, nπ, where n = 0, 1, 2,...

In degrees, the sin is zero at 0, 180, 360, etc.

 

[Neon32]

A node is a location where the amplitude is zero. The sin function is zero when its argument is a multiple of π radians, nπ, where n = 0, 1, 2,...

In degrees, the sin is zero at 0, 180, 360, etc.

Ok I understood this part but which one is the amplitude "Y" or "A"?

and can I take the angle of cos and make it equal to n pi/2 where n is odd number? It will also give me 0 in this case.

 

[pixel]

I probably shouldn't have used the word "amplitude" for y. y is the displacement for a given x,t, whereas the amplitude is the maximum value of y.

Those values of x that lead to the argument of sin being nπ will give y = 0 for all t. Will have to think about your question of setting the cos argument to nπ/2.

 

[pixel]

Okay, check out the section Two sine waves traveling in opposite directions create a standing wave at: http://www.acs.psu.edu/drussell/Demos/superposition/superposition.html

If the argument of the cos is nπ/2, then those values of t lead to y = 0 for all x. That is shown in the simulation on the referenced web page.

 

[PeterO]

Ok I understood this part but which one is the amplitude "Y" or "A"?

and can I take the angle of cos and make it equal to n pi/2 where n is odd number? It will also give me 0 in this case.

An over view:
The argument of the sin includes an "x", leading to where (along the string) the function is zero.
The argument of the cos includes a "t" leading to when (in time) the function is zero.
The question related to where the nodes were, so work with the sin.
In a standing wave, even points of antinode are periodically at zero displacement - when that happens is found by playing with the cos function

 

[pixel]

In a standing wave, even points of antinode are periodically at zero displacement - when that happens is found by playing with the cos function

That's shown in the simulation I referenced.