Write an expression for the angular frequency of the wave, and hencerelate β to the speed of light in vacuum c.

The angular frequency (ω) of a wave is related to its frequency (f) by the equation:

ω = 2πf

The wave number (β) is related to the wavelength (λ) by the equation:

β = 2π/λ

The speed of light in vacuum (c) is related to the frequency and wavelength of the wave by the equation:

c = fλ

Substituting the expressions for ω and β into the equation for c gives:

c = (ω/2π)(2π/β)

Simplifying this gives:

c = ω/β

So, the wave number β is related to the speed of light in vacuum and the angular frequency by the equation:

β = ω/c