Equivalent Network Models of Continuous Media and a Network Representation of Sound Radiators

Abstract

Simple acoustical systems may often be treated as acoustical networks with lumped elements if the linear dimensions of the elements are small compared with the wavelength. At higher frequencies this circuit theory method becomes less practical, and it is then necessary to use a field theory where the medium is considered continuous. It is sometimes difficult to decide whether to use the circuit theory approach or the field theory approach, because the accuracy obtainable with the circuit theory and lumped elements is not immediately apparent. It is shown in the paper that much uncertainty may be resolved by careful analysis of the elements used in the circuit theory. This is demonstrated by means of a simple example. In the design of sound radiators it is often convenient to represent the radiation impedance as a lumped element network, and such representations are well known for simple sound sources. When an extended definition of radiation impedance is used it becomes possible to find a simple network representation of spherical sound sources of arbitrary order n. Examples are given for n = 0,1,2 … 7. A simple network representation is also possible for the input impedance of exponential and hyperbolic horns. The physical significance of these representations is discussed.