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.

 

[Bastinium]

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.

For multiplexing discreet digital data packets with exceptional resolution and quality without inferential degeneracy degradation

 

[berkeman]

For multiplexing discreet digital data packets with exceptional resolution and quality without inferential degeneracy degradation

I may be misunderstanding your thread start and reply, but no. You cannot encode lots more information in harmonics. To encode more information you need to choose orthogonal and non-harmonic frequencies to be able to use unique data decoding.

https://en.wikipedia.org/wiki/Spread_spectrum

https://en.wikipedia.org/wiki/Orthogonal_frequency-division_multiplexing

 

[Bastinium]

I may be misunderstanding your thread start and reply, but no. You cannot encode lots more information in harmonics. To encode more information you need to choose orthogonal and non-harmonic frequencies to be able to use unique data decoding.

https://en.wikipedia.org/wiki/Spread_spectrum

https://en.wikipedia.org/wiki/Orthogonal_frequency-division_multiplexing

Octavial Frequency Integration (OFI) multiplexing was just born today. LoL

 

[Ibix]

Octavial Frequency Integration (OFI) multiplexing was just born today. LoL

Not sure if you're joking or missing the point. Precisely because resonant frequencies are resonant, it's harder to use resonant devices to distinguish them. Hence you want your carrier frequencies to be as far from resonant with each other as you can arrange.

 

[Bastinium]

Not sure if you're joking or missing the point. Precisely because resonant frequencies are resonant, it's harder to use resonant devices to distinguish them. Hence you want your carrier frequencies to be as far from resonant with each other as you can arrange.

But it can be distinguished