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wave number

dwsmith

Well-known member
Feb 1, 2012
1,673
$\sin nx$

Is the wave number $n$ or $\frac{2\pi}{n}$?
 

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621
$\sin nx$

Is the wave number $n$ or $\frac{2\pi}{n}$?
Is \(n\) represent the wavelength? Then there are two definitions for the spectroscopic wave number and angular wave number.

Kind Regards,
Sudharaka.
 

dwsmith

Well-known member
Feb 1, 2012
1,673
Is \(n\) represent the wavelength? Then there are two definitions for the spectroscopic wave number and angular wave number.

Kind Regards,
Sudharaka.
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 $\sin nx$.
 

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621
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 $\sin nx$.
What did your professor tell and what is the context of this question. Can you please explain?
 

dwsmith

Well-known member
Feb 1, 2012
1,673
What did your professor tell and what is the context of this question. Can you please explain?
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, $k = n$.
 

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621
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, $k = n$.
So, \(k=n=\frac{2\pi}{\lambda}\) is the wave number.