dispersion relation

A dispersion relation describes how waves of different wavelengths or frequencies propagate through a medium. It relates the wave's frequency (how fast it oscillates) to its wavelength (the distance between wave peaks). This relationship determines how waves behave; for example, whether they move at different speeds or change shape as they travel. Understanding dispersion relations helps us analyze phenomena like light spreading in prisms, sound waves in air, or water waves in the ocean, by predicting how these waves will evolve based on their specific properties and the medium they move through.