Harmonic Orders

[Bastinium]

I'm looking for a mathematical representation of a fundamental wave and it's harmonic modes.
For example a wave of 590 nm what are its 'octaves'?

Can the resulting formula be represented in polar coordinate 'vector' space?

 

[Ibix]

I'm not sure what you are asking.

A single monochromatic wave is described by a sine wave, $A\sin(\omega t-kx)$, where $\omega=ck$, $k=2\pi/\lambda$, $\lambda$ is the 590nm you specified, and $A$ is the amplitude (how bright the light is, roughly).

Octaves are double the frequency (i.e. half the wavelength), so would be the same thing but with $\lambda$ in nm being 590/2, 590/4, 590/8 etc.

Does that help?

 

[Bastinium]

I'm not sure what you are asking.

A single monochromatic wave is described by a sine wave, $A\sin(\omega t-kx)$, where $\omega=ck$, $k=2\pi/\lambda$, $\lambda$ is the 590nm you specified, and $A$ is the amplitude (how bright the light is, roughly).

Octaves are double the frequency (i.e. half the wavelength), so would be the same thing but with $\lambda$ in nm being 590/2, 590/4, 590/8 etc.

Does that help?

Resonant conjuncts, like in music...

 

[Ibix]

Resonant conjuncts, like in music...

Yes - those are integer or half-integer frequency multiples as I described. They're less interesting in optics than in music because our visual range is a bit less than one octave so we can't see any (at least, not any fundamentals).

We can exploit resonant cavities for various applications - anti-reflection coatings on lenses and optical filters used in optical fibre communications work that way, as do the colours in an oil film on water. And interference effects are related phenomena that lead to the rainbow colours on CDs as well as the colours on some bird feathers and butterflies.