Derivation of y(x,t)=Asin(kx-wt)

[Point Conception]

Can someone show, or explain with a diagram, how y(x,t)=Asin(kx-wt)
is a solution of the wave equation. In particular how for a given (y) value that
(kx-wt) is a constant.

 

[willem2]

This isn't the full solution. The full solution is a superposition of solutions
Asin(kx - wt + C), with different A's, k's, w's and C's, subject only to w/k=
(propagation speed of wave)

In particular how for a given (y) value that
(kx-wt) is a constant.

I don't understand this at all. y depends on x and t, and so does (kx-wt)

 

[Vanadium 50]

Can someone show, or explain with a diagram, how y(x,t)=Asin(kx-wt)
is a solution of the wave equation. In particular how for a given (y) value that
(kx-wt) is a constant.

If y and A are constant, so is arcsine(y/A). That should get you going.