(a) Define the terms wavelength λ, wave number k, frequency ν and angular frequency ω for an electromagnetic wave.
(b) Starting from the fundamental definitions of λ, ν, k and ω, prove that for an electromagnetic wave in vacuum the product of wavelength and frequency is a constant equal to the speed of light.
(c) Explain physically why this constancy implies that if the frequency of such a wave is doubled, its wavelength must be halved.