# wave number

#### dwsmith

##### Well-known member
$\sin nx$

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

#### Sudharaka

##### Well-known member
MHB Math Helper
$\sin nx$

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
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
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
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
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.