Applications of the Helmholtz equation

Abstract

In this paper, we are talking about the Helmholtz equation and its physical meaning. Helmholtz equation is used to solve problems in physics such as seismology, electromagnetic radiation, and acoustics. It applies to a wide variety of situations that arise in electromagnetics and acoustics. It is also equivalent to the wave equation assuming a single frequency. In water waves, it arises when we Remove The Depth Dependence. Often there is then a cross over from the study of water waves to the study of scattering problems more generally. Also, if we perform a Cylindrical Eigenfunction Expansion we find that the modes all decay rapidly as distance goes to infinity except for the solutions which satisfy Helmholtz's equation. This means that many asymptotic results in linear water waves can be derived from results in acoustic or electromagnetic scattering.