Considering the definition of wavelength, frequency and propagation speed, if the wavelength is doubled, the frequency is reduced by half.
In a periodic wave the wavelength (λ) is the physical distance between two points from which the wave repeats itself. That is, the wavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).
The frequency (f) is a measure of the number of cycles or repetitions of the wave per unit of time. Its unit is s⁻¹ or hertz (Hz).
The wavelength and its frequency are related from the speed at which the wave travels. The propagation speed (v) is the speed with which the wave propagates in the medium, that is, it is the magnitude that measures the speed at which the wave's disturbance propagates along its displacement. So, the speed expression is:
v=λ×f
This indicates that the higher the frequency, the shorter the wavelength and the lower the frequency, the longer the wavelength.
All electromagnetic waves propagate in a vacuum at a constant speed of 300,000,000 m/s, the speed of light. Then, since an inversely proportional relationship is established between the frequency and the wavelength, if the wavelength is doubled, the frequency is reduced by half.
In summary, if the wavelength is doubled, the frequency is reduced by half.
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