Question about traveling waves

[Johnny5]

Is it possible to derive the formula for a traveling wave using classical Newtonian mechanics? Here is the formula I want to derive:

 

[math] A(x,t) = A_0 sin(kx-\omega t ) [/math]

 

Thank you

[swansont]

I don't think you can derive it - it's a definition.

[Johnny5]

I don't think you can derive it - it's a definition.

 

No I derived it years ago using the galilean transformations, but I forgot what I did. I was hoping someone here might have done the same thing, or have a different argument, reaching the same formula.

 

Regards

 

PS The argument went something like this.

 

Start with the sine function:

 

y = sin x

 

The maximum amplitude is 1. Now, let the amplitude be arbitrary:

 

[math] y = A_0 sin x [/math]

 

Now, fix your attention on a point on the wave, at x = 90 degrees=pi/2 radians

 

sin (90 degrees) = 1

A0 sin (90) = A0

 

So the coordinates of the point on the wave are:

 

(x,y) = (pi/2,A0)

 

Now, the wave is supposed to travel in the direction of increasing coordinates, so that this point on the waveform must have some velocity v, in that direction. Work fowards from here. Has anyone ever seen this derivation?

[swansont]

Start with the sine function:

 

y = sin x

 

OK. You didn't say you were starting here - it sounded like you wanted to derive it from first principles.

[Johnny5]

OK. You didn't say you were starting here - it sounded like you wanted to derive it from first principles.

 

Have you ever seen the kind of derivation I am asking about?

 

Regards

[swansont]

Yes, but I don't recall the details. It was a while ago.