0

I'm looking for a function that I can use to plot a sinusoidal wave for various color frequencies. For example, the frequency of red light is 4.6 THz (4.6*10^14 Hz). The frequency of blue light is 6.3 THz (6.3*10^14 Hz). I'm not sure how I can translate these frequencies into sine functions, however, despite a fair amount of searching online. I'd appreciate any guidance toward the right direction. Here's an example:

enter image description here

littleK
  • 101
  • The wavelength in microns is $ \ \frac{3.00 \cdot 10^{14}}{f} \ $ with the frequency $ \ f \ $ in Hertz. Incidentally, 4.6 THz is $ \ 4.6 \cdot \ 10^{12} \ $ , not $ \ 10^{14} \ $ . I believe you mean 460 THz. – colormegone Jan 25 '16 at 05:29
  • If you want to make sine functions with wavelengths in units of microns (your picture uses cosine functions), and you're not fussy about things like phase, you can use $$ \ y \ = \ \sin( 2 \pi \ [\frac{f}{3.00} ] \ x ) \ \ , $$ with frequency $ \ f \ $ in units of $ \ 10^{14} \ $ Hz. For $ \ f \ = \ 4.6 \ $ (your red), you should get a cycle of 0.652 units on your graph, which will be microns. For $ \ f \ = \ 6.3 \ $ (your blue) , you should get 0.476 units. I'm using an amplitude of 1 for the sine function; you can multiply the function by some number to vary the "height" of the graphs. – colormegone Jan 25 '16 at 05:44
  • This is perfect, thank you! Please convert this comment to an answer and I'll accept it! – littleK Jan 25 '16 at 17:45

1 Answers1

1

Converting colormegone's comment into an answer so it can be accepted:

If you want to make sine functions with wavelengths in units of microns (your picture uses cosine functions), and you're not fussy about things like phase, you can use $$y=\sin\left(2\pi\left[\frac{f}{3.00}\right]x\right),$$ with frequency $f$ in units of $10^{14}$ Hz. For $f=4.6$ (your red), you should get a cycle of 0.652 units on your graph, which will be microns. For $f=6.3$ (your blue), you should get 0.476 units. I'm using an amplitude of 1 for the sine function; you can multiply the function by some number to vary the "height" of the graphs.

Robert Howard
  • 2,753