- #1

nietzsche

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Hi everyone,

I'm trying to understand the derivation of

[tex]D(x,t) = A \sin{(kx - \omega t + \phi_o)}[/tex]

which is the displacement equation for a sinusoidal wave.

The way my textbook (Physics for scientists and engineers by Knight) does it:

Look at the graph of displacement versus position at time t = 0. The function that describes this graph is

[tex]D(x,t=0) = A \sin{(2 \pi (\frac{x}{\lambda}) + \phi_o)}[/tex]

Now what I don't get is the next step. We replace x with the quantity (x-vt), where v is the speed of the wave. The resulting equation is

[tex]D(x,t) = A \sin{(2 \pi (\frac{x-vt}{\lambda}) + \phi_o)}[/tex]

Where does this (x-vt) term come from? I don't understand what this equation means, because I thought we were considering t = 0, and now we are throwing in a t variable.

Please help me understand! Thanks in advance.

edit: I found this: http://en.wikipedia.org/wiki/D'Alembert's_formula

I think it is related, but I don't understand the article at all...

I'm trying to understand the derivation of

[tex]D(x,t) = A \sin{(kx - \omega t + \phi_o)}[/tex]

which is the displacement equation for a sinusoidal wave.

The way my textbook (Physics for scientists and engineers by Knight) does it:

Look at the graph of displacement versus position at time t = 0. The function that describes this graph is

[tex]D(x,t=0) = A \sin{(2 \pi (\frac{x}{\lambda}) + \phi_o)}[/tex]

Now what I don't get is the next step. We replace x with the quantity (x-vt), where v is the speed of the wave. The resulting equation is

[tex]D(x,t) = A \sin{(2 \pi (\frac{x-vt}{\lambda}) + \phi_o)}[/tex]

Where does this (x-vt) term come from? I don't understand what this equation means, because I thought we were considering t = 0, and now we are throwing in a t variable.

Please help me understand! Thanks in advance.

edit: I found this: http://en.wikipedia.org/wiki/D'Alembert's_formula

I think it is related, but I don't understand the article at all...

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