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Is \(n\) represent the wavelength? Then there are two definitions for the spectroscopic wave number and angular wave number.$\sin nx$
Is the wave number $n$ or $\frac{2\pi}{n}$?
I looked at that page but it didn't really help. My prof said one thing and that says something else so I was hoping someone could just say this how it is determined from $\sin nx$.Is \(n\) represent the wavelength? Then there are two definitions for the spectroscopic wave number and angular wave number.
Kind Regards,
Sudharaka.
What did your professor tell and what is the context of this question. Can you please explain?I looked at that page but it didn't really help. My prof said one thing and that says something else so I was hoping someone could just say this how it is determined from $\sin nx$.
Wave equation.What did your professor tell and what is the context of this question. Can you please explain?
So, \(k=n=\frac{2\pi}{\lambda}\) is the wave number.Wave equation.
So we have after separation of variables
$$
\frac{T'' + 2T'}{T} = \frac{X''}{X} = -k^2
$$
He said $k$ is the wave number which implies n is the wave number for certain boundary conditions. In my case, the eigenfunction is $X = \sin k\pi = 0$. Therefore, $k = n$.