Acoustics-A Textbook for Engineers and Physicists by Jerry H. Ginsberg

Author:Jerry H. Ginsberg
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(3.4.9)

Substitution of the state variables in Eq. (3.4.8) into the preceding yields a set of four simultaneous equations for the four complex amplitudes. Each equation is linearly independent, so we may proceed to their solution. This usually is done with mathematical software, which is aided by collecting the wave amplitudes in a column vector. The coefficients of the algebraic equations form a square matrix . The result is

(3.4.10)

where

(3.4.11)

Thus, at each frequency, we would evaluate and form solve for the four unknown wave amplitudes, and then use the solution to evaluate any desired properties of the acoustic field.

If there are N segments, then the pressures within the network are represented by a total of 2N amplitudes. The junction and termination conditions will extend Eq. (3.4.10) to 2N equations. For example, suppose there are three branches with a single junction as in Fig. 3.11. Conservation of mass at the junction gives one equation. Two more equations are obtained from setting Three more equations are obtained from the condition at the termination of each branch, and the last imposes the excitation.

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