Traditional methods for the investigation of sound fields generally rely on a microphone to convert sound pressure into an electrical signal which can be recorded, displayed, and so forth. The squared sound pressure is directly related to potential energy density. Consequently, the measurement of sound pressure alone does not inherently provide insight into the total energy density of the sound field. Specifically, no information about the kinetic energy density of the sound field is available from this measurement alone. However, it is possible to use two microphones to estimate particle velocity. The squared particle velocity magnitude is directly related to kinetic energy density. The two energy quantities combine to yield total acoustic energy density.

The purpose of this work is to investigate and compare three probes designed to measure acoustic energy density. It is also to determine which probe may be most practically implemented in real-world applications. All three designs are based on a rigid spherical housing and are referred to as follows: the six microphone probe, the tetrahedron probe, and the orthogonal probe. The six microphone probe is so named because it is made up of six microphones, with one pair of microphones oriented along each Cartesian axis. The tetrahedron probe is so named because it has four microphones, one at each of the vertices of a regular tetrahedron. The orthogonal probe has four microphones positioned in such a way that the lines drawn from an origin microphone to the other microphones form an orthogonal set.

The majority of the work presented in this thesis uses Matlab to numerically predict the behavior of the probes. Four numeric models are used to predict the behavior of the three different probes. The models match the geometric arrangement of the various probes. A simple experiment also shows how the probes respond to a source in an anechoic environment.

The results of the numeric modeling indicate that the orthogonal probe has the greatest useable frequency range. Both the tetrahedron and the orthogonal probes have a greater frequency range than the six microphone probe. However, in the simple experiment, the orthogonal probe did not measure energy density as accurately as the tetrahedron probe when the orthogonal probe was rotated, such that no Cartesian axis was parallel to the radial axis of the source. The data indicate that more work must be done before a decision can be made between the tetrahedron probe and the orthogonal probe. It is clear that it is possible to measure acoustic energy density in 3-dimensions using only four microphones, instead of six.



College and Department

Physical and Mathematical Sciences; Physics and Astronomy



Date Submitted


Document Type





acoustic, energy, density