Abstract
The acoustic wave most commonly transmitted and detected in the high-porosity absorbent materials used in noise control is generally the air-borne slow compressional wave. In a new experiment, the air saturating the sample is replaced by helium and the transmission is studied at ultrasonic frequencies (70–600 kHz). The experiment is quite easily performed using standard ultrasonics and vacuum equipment. The main purpose of this work is to propose a method to determine simultaneously both the viscous and thermal characteristic lengths with the same precision. These two parameters characterize the viscous and the thermal interactions between the frame and the fluid at high frequencies. The characteristic lengths are deduced from the high-frequency asymptotic behavior of either the velocity or the attenuation curves obtained in the sample saturated by air and by helium. It also appears that due to the properties of helium, the discrepancy previously observed between predictions and measurements is shifted toward higher frequencies.
Highlights
A very particular prediction of the theory established by Biot[1] in 1956 on the acoustics of fluid-saturated porous media is the existence of a second compressional wave in consolidated media
Nagy, Adler, and Bonner[8] have shown that it is possible with a standard experimental setup to detect a slow compressional wave in both artificial and natural rocks saturated by air in a frequency window where the mode is propagative and not too heavily attenuated
The quantity␥Ϫ1͒/B is equal to 0.815 in helium and 0.475 in air. Using these numerical values and assuming that the order of magnitude of ⌳Ј is approximately double that of ⌳, it can be calculated from Eq ͑1͒ that the ratio VHe/Vair of the limit velocities of the slow wave when the sample is saturated by helium and by air is approximately 2.9 while the ratio of attenuation is about 1.1 ͓Eq. ͑1͔͒
Summary
A very particular prediction of the theory established by Biot[1] in 1956 on the acoustics of fluid-saturated porous media is the existence of a second compressional wave in consolidated media. Nagy, Adler, and Bonner[8] have shown that it is possible with a standard experimental setup to detect a slow compressional wave in both artificial and natural rocks saturated by air in a frequency window where the mode is propagative and not too heavily attenuated. This window is rather narrow for air-saturated materials because of the high kinematic viscosity of air. It is set by the condition that the viscous skin depth, ␦ ϭ ͱ2/ at the angular frequency , must be less than the pore size while the wavelength must be greater than the grain size.[8]
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