longitudinal wave equation

A longitudinal wave equation describes how pressure and particle displacement change as a wave travels through a medium, like air or water. In these waves, particles move back and forth along the wave's direction, creating regions of compression and rarefaction. The equation mathematically relates the pressure variation to the displacement of particles and the properties of the medium, such as density and elasticity. It helps predict wave behavior—like speed, amplitude, and shape—by capturing how these quantities evolve over space and time, ensuring a precise understanding of phenomena like sound waves.