All waves on the electromagnetic spectrum travel at the same speed in a vacuum. the speed of these waves in a vacuum is 3x108 m/s. as the wavelength of wave doubles, how does the speed and frequency of the wave change

The wavelength (λ), speed (c) and the frequency (ν) of a wave are related as:

ν = c/λ  (1)

The speed of the waves is a constant in vacuum i.e. it remains at 3*10⁸ m/s. therefore, it will not change with changes in wavelength or frequency.

Let us consider:

ν1 = initial frequency and λ1 = initial wavelength

ν2 = final frequency and λ2 = final wavelength = 2(λ1)

based on equation (1) we have:

ν1/ν2 = λ2/λ1 = 2(λ1)/λ1 = 2

therefore: ν2 = 1/2(ν1)

The frequency will get reduced by one-half as the wavelength doubles.