The relationship between wavelength and frequency is an inverse one: as the wavelength of a wave increases, its frequency decreases, and vice versa. This is because the speed of a wave (v or c for electromagnetic waves) is the product of its frequency (f) and wavelength (λ), expressed by the equation:

v=fλv=f\lambda v=fλ

If the wave speed is constant in a given medium, increasing the frequency means the wavelength must decrease to keep the product constant, and decreasing the frequency means the wavelength increases

. For example, in electromagnetic waves traveling in a vacuum, the speed of light ccc is constant (~3×1083\times 10^83×108 m/s), so:

c=fλc=f\lambda c=fλ

Here, higher frequency waves (like gamma rays) have very short wavelengths, while lower frequency waves (like radio waves) have very long wavelengths

. In summary:

• Wavelength (λ) and frequency (f) are inversely proportional.
• Their product equals the wave speed (v or c).
• This relationship explains phenomena such as the different colors of visible light, where blue light has a higher frequency and shorter wavelength than red light

This fundamental wave relationship applies broadly to sound waves, electromagnetic waves, and other wave types.