wave number

[dwsmith]

$\sin nx$

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

 

[Sudharaka]

$\sin nx$

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]

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]

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]

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]

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.