New method for measurement of the total energy density of sound waves

Abstract

The total energy of a sound field in reverberation chambers is usually sampled by an array of microphones. Each measures the time average of the squared sound pressure at its location. This is equivalent to sampling the time average of the potential energy density of the sound field. It would be advantageous to measure as well the time-averaged squared particle velocity. This would yield the kinetic-energy density, which added to the potential-energy density would then yield the total-energy density. A principal advantage of the total energy density is that its spatial variance is in general appreciably less than the potential variance. We find this from an analysis of the variances for the eigenmodes of rectangular chambers having reflecting (rigid) walls. A microphone for total energy density can be made from a spatial array of four elements arranged at the corners of a tetrahedron. Electret microphones seem to be particularly suitable for the elements. The total energy density can be computed from the sums and differences of the electret outputs, with the help of integrated circuits, and displayed as a running function of time, e.g., as a graphic recording. For a standing-wave tube, only two elements are needed, and the total-energy-density microphone then takes a very simple form.