[themonk]

I have this equation and I have to prove that it is true.

$$y(x,t) = A*sin(\frac{2*\pi}{\lambda}*(x-v*t))$$
(I'm sorry but I cannot get the LaTeX to work) - http://www.codecogs.com/latex/eqneditor.php

I do not want to start and obviously don't want people to tell me how to finish the problem, but I just need a hint as to what to look for or do.

I know that the lambda is the wavelength, the v is the velocity (to the right) and that the frequency is mu which is equal to v/lambda.

I probably have to find another equation for y(x,t) (?) but reading through the book (Quantum Chemistry McQuarrie) is getting difficult and very confusing.

[Borek]

Your LaTeX looks OK to me. Check if you have Java enabled in your browser.

[themonk]

Perfect.

And on a better note, I think I actually figured it out. Let me know what you think:

I took the derivative in terms of $$\frac{d^{2}y}{dx^{2}}$$ and $$\frac{d^{2}y}{dt^{2}}$$

Then setting them equal to each other using the this definition:
$$\frac{d^{2}y}{dx^{2}} = \frac{1}{v^{2}} \frac{d^{2}y}{dt^{2}}$$

and solving showing that they are equal, therefore saying that the wavelength is lambda.

I actually worded the original question quite badly. I was putting it in my own words, but I had to prove that lambda was the wavelength for the equation given, that the frequency was mu=v/lambda, and that the velocity goes to the right. I figured out the other parts also (I hope), but won't worry about it too much.

[juanrga]

Perfect.

And on a better note, I think I actually figured it out. Let me know what you think:

I took the derivative in terms of $$\frac{d^{2}y}{dx^{2}}$$ and $$\frac{d^{2}y}{dt^{2}}$$

Then setting them equal to each other using the this definition:
$$\frac{d^{2}y}{dx^{2}} = \frac{1}{v^{2}} \frac{d^{2}y}{dt^{2}}$$

and solving showing that they are equal, therefore saying that the wavelength is lambda.

I actually worded the original question quite badly. I was putting it in my own words, but I had to prove that lambda was the wavelength for the equation given, that the frequency was mu=v/lambda, and that the velocity goes to the right. I figured out the other parts also (I hope), but won't worry about it too much.

Only a comment, total derivatives must be replaced by partial ones.