Absolute calibration of acoustic sensors utilizing electromagnetic scattering from in situ particulate matter

Abstract

The present paper initiates a study to understand the errors inherent to a laboratory technique similar to that used by K. J. Taylor [J. Acoust. Soc. Am. 70, 939–945 (1981)] for absolute calibration of microphones. Considered here is the idealized situation when a plane-polarized monochromatic plane electromagnetic wave is incident on a finite scattering volume containing dispersed small dielectric spheres that oscillate under the joint influence of a plane transient acoustic wave and Brownian motion. Any component of the scattered and Doppler-shifted electromagnetic signal at a distant farfield point in an obliquely backward direction is a sum of N terms, each of the generic form An cos(ω0t) + Bn sin(ω0t), where An and Bn depend on the instantaneous position of the nth scatterer. Since these positions change with time, the coefficients also vary, although slowly over intervals comparable to 1/ω0. Statistical properties of the time varying sum functions A(t) and B (t) are studied analytically and with numerical simulations for various models of the sound wave and the Brownian motion. A principal problem adressed is that of determining the statistics of the time interval Δt over which a fixed number K of zero crossings occur for the sum A(t) cos(ω0t) + B(t) sin(ω0t), given that this interval is centered at a particular time, the pertinent quantity of interest being the relative error in the accumulative phase difference 2 π K / Δt − ω0 per unit time. The results support the general conclusions that smaller errors are expected for higher amplitude sound waves and for sound waves of lower frequency. [Work supported by ONR.]