A model for the holographic reconstruction of sound fields disturbed with temperature gradients

Abstract

Holographic techniques are used to detect noise sources in a wide range of devices. Some of these techniques are commonly employed in the reconstruction of sound fields produced by automobile or motorcycle engines. These sound fields are characterized by having several, rather than single, temperatures; in fact, temperature gradients are frequently found in regions near the engine. These gradients produce changes in every point of the sound wave velocity. The mathematical model presented in this paper was designed to minimize the effect of assuming a constant sound velocity in the entire space in reconstruction of the sound field. It is based on the space transformation of sound field (STSF) technique [Hald, Jo/rgen, B&K Tech. Rev. 1, 1–50 (1989)], which uses a microphone array to measure pressure or determine the principal component of cross spectra over a hologram plane. The model scans the sound field in two planes. The first plane is used as an STSF initial condition (hologram plane), and the second plane is considered the boundary condition to Rayleigh integral’s propagation.