A Plane Wave Superposition Method: Modeling Acoustic Fields Inside Cavities

Open Access
Kamrath, Matthew James
Graduate Program:
Master of Science
Document Type:
Master Thesis
Date of Defense:
March 18, 2014
Committee Members:
  • Gary Hugo Koopmann, Thesis Advisor
  • Acoustics
  • Plane Waves
  • Cavities
The Plane Wave Superposition Method (PWSM) presented here simply and efficiently calculates the pressure and velocity fields inside an arbitrarily shaped cavity with mixed boundary conditions and internal acoustic sources. In this boundary value problem, a superposition of N plane wave represents the acoustic pressure field, and the boundary conditions at N locations approximates the continuous boundary conditions. The solution’s sensitivity and accuracy is evaluated using the condition number and the maximum error in the boundary conditions. The PWSM’s theory is illustrated using the following six examples: a one-dimensional tube, a circle, a square, a trapezoid, a sphere, and a cube where the pressure is specified on the boundaries. The tube example demonstrates that the PWSM and an analytic method give the same solution in one-dimensional problems. In all of the two and three dimensional examples, the continuous boundary conditions are well approximated with a finite number of points over a wide range of frequencies. The examples also illustrate that the condition number is proportional to the non-dimensional wavenumber and the number of points per wavelength used to approximate the boundary conditions. Further, the approximation’s accuracy is inversely proportional to the number of points per wavelength that are used to approximate the boundary conditions.