Interference between direct and ground-reflected waves over grass in the presence of atmospheric turbulence

Abstract

In a previous paper [G. A. Daigle. J. E. Piercy and T. F. W. Embleton, J. Acoust. Soc. S14–S15. (1977)] measurements of the interference spectrum between direct and ground-reflected waves, at distances up to 150 ft over a flat asphalt surface, were shown to be in satisfactory agreement with a theory that included a known degree of partial covariance between the phases of the interfering waves. The amount of covariance was calculated from measurements of wind and temperature fluctuations in the atmosphere. This theory has now been extended to include propagation over ground of finite acoustic impedance and provides an explanation of the measurements of Parkin and Scholes over grass [J. Sound Vib. 2, 353–374 (1965)] to a distance of 1100 m. Above 300 Hz the sound levels reported by Parkin and Scholes are up to 10 dB higher than predicted by coherent acoustic theory. Although the fluctuations of wind and temperature were not reported, agreement is obtained by assuming standard deviations in phase velocity of about 1 in 1000 and correlation lengths of about 1 m—typical of values measured recently in Ottawa. Covariance of sound amplitude is relatively more important at long distances—at short distances its effect is negligible compared with that of phase covariance; phase-amplitude covariance is negligible at all distances.