Kinetic and potential energies of a stationary sound field

Abstract

There is a continuing need for accurate measurement of radiated sound power by compact noisy sources. Examples are the noises of fans, motors, machinery, etc. One of the standard methods of measurement makes use of a reverberation chamber. The potential energy of the sound radiated into the chamber is measured by sampling the sound pressure at various points, from which the time-space-averaged potential energy is calculated. The kinetic energy is assumed to equal the potential energy; then in the standard method, the sum of the two is used as the total energy for calculation of the radiated sound power. In experiments on a source having an accurately known radiated power, we found that the power determined in a standard-method chamber was about 20% (0.9 dB) less than the true power. A likely source of the systematic difference is the possibly false assumption that the time-space averaged kinetic energy is equal to the potential energy. It is shown that, in general, in a sound field stationary in an enclosure, the two energies are not equal. Several examples are presented. Included are fields in enclosures having sound absorbers. An accurate ratio of the energies requires detailed knowledge of the field.