The wavelength of an electromagnetic (EM) wave is inversely proportional to its frequency. This relationship is described by the equation:
wavelength = speed of light / frequency
where the speed of light is a constant.
If we double the frequency of an EM wave while keeping the speed of light constant, the wavelength will be halved. Conversely, if we halve the frequency, the wavelength will be doubled.
To illustrate this relationship, let's consider an example with an arbitrary frequency and wavelength. Suppose we have an EM wave with a frequency of 100 MHz (megahertz), which corresponds to a wavelength of 3 meters (assuming the speed of light is approximately 3 x 10^8 meters per second). If we double the frequency to 200 MHz, the wavelength will be halved to 1.5 meters. On the other hand, if we halve the frequency to 50 MHz, the wavelength will double to 6 meters.
In summary, doubling the frequency of an EM wave results in halving its wavelength, while halving the frequency leads to doubling the wavelength. This relationship holds true for the entire electromagnetic spectrum, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.