Electromagnetic Waves $f(t)= A\sin Bt$

Question

I recently saw this question which was slightly lacking in formulation, but I was still interested in solving it; but I can't.

Light be seen as electromagnetic waves, which in vacuum, moves with the speed of $3,0\times10^8$m/s. The waves can be described using the formula: $f(t)=A\sin Bt$. What is the value of $B$ for blue light with the estimated wavelenght of $450$nm and yellow light with the estimated wavelenght of $580$nm?

I tried using the standard wavelenght equation, but fell short.

Answer 1

You can write this equation as $$f(t)=A\sin(2\pi f t)$$ The relationship between frequency of the light $(f)$, wavelength $(\lambda)$, and speed $(c)$ is $$c=\lambda f$$ From here $$f=\frac{c}{\lambda}$$ and therefore $$B=2\pi\frac{c}{\lambda}$$ For blue light $B=4.19\cdot 10^{15} s^{-1}$ and for yellow $B=3.25\cdot 10^{15} s^{-1}$ I've used $1 nm=10^{-9}m$