Waves in ducts described by means of potentials

Abstract

The waveguide theory constitutes an important part of classical wave theory and the results are applied in many practical devices. The aim of the paper is to present a coherent approach to the problem of propagation of sound and electromagnetic waves in ducts by means of potentials. The potential concept simplifies the field description and discussion of some basic conditions, posed on mathematical expressions, which come from their physical meaning. These conditions are, for example, the Euler equation for sound waves or the Lorentz gauge condition for electromagnetic field. The analyze of the respected field is carried out by means of velocity potential for sound waves and the Hertz potentials for electromagnetic waves. The acousto-electromagnetic analogies are derived and discussed for infinite circular and rectangular duct. The cut-off frequencies, the waveguide impedance and the power transmitted along the duct is discussed in reference to these analogies.