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- Thread starter dwsmith
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- Feb 5, 2012

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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 $\frac{2\pi}{n}$?

Kind Regards,

Sudharaka.

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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.

- Feb 5, 2012

- 1,621

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 $\sin nx$.

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Wave equation.What did your professor tell and what is the context of this question. Can you please explain?

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, $k = n$.

- Feb 5, 2012

- 1,621

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, $k = n$.