Acoustic modes

Each member of the family of acoustic elements is used to model an organ pipe. The natural modes of vibration are extracted from the models for the case of an organ pipe with both ends open (open/open) and the case of an organ pipe with one end open and the other end closed (open/closed). The appropriate boundary condition at an open end is that the acoustic pressure degrees of freedom be set to zero (a free surface). A closed end requires no boundary condition; the natural boundary condition is that of a rigid surface adjacent to the fluid. Results are compared with exact solutions.

The model consists of a column of air 165.8 units high with a cross-sectional area of 1.0. The first-order element model consists of 20 acoustic elements along the length of the fluid column and one through the cross-section. The second-order element models consist of 10 elements.

The material properties used for the air are ${\rho }_f$ = 1.293 and bulk modulus = 1.42176 × 10⁵.

The models consist of duct-like meshes of length 0.1. The first step consists of an eigenvalue analysis of the model with no boundary conditions. The second step applies a spherical nonreflecting impedance on all exterior ends of the ducts. The third step performs an eigenvalue analysis of the model with the impedance conditions. Results are printed only for the first and third steps.

The models consist of duct-like meshes of length 0.1, terminated with acoustic infinite elements. The first analysis step consists of a real eigenvalue analysis of the model. The second step performs a complex eigenvalue analysis of the model.