A second bulk compressional wave has been observed in a water-saturated porous solid composed of sintered glass spheres using an ultrasonic mode conversion technique. The speed of this second compressional wave was measured to be 1040 m/sec in a sample with 18.5% porosity. The theory of Biot, which predicts two bulk compressional waves in porous media, provides a qualitative explanation ofthe observations. To the author's knowledge, this type of bulk wave has not been observed at ultrasonic frequencies.

PHYSlCAL REVIEW LETTERS 20 DECEMBER 1982 measurement (such as a, study of the oscillation of a cylindrical cavity containing SPH), the b state will show a much smaller effective superfluid density and will produce a lot more damping than the a state. I thank Andrei Huckenstein and Eric Siggia for discussions. I also thank David Mermin for urging me to reformulate my original. presentation in a more general form. This work is supported by the National Science Foundation, Grant No. PH Y77-27084.

We have investigated the ultrasonic properties of unconsolidated (loose) glass beads and of lightly fused (consolidated) glass beads when the pore space is saturated with water. At a frequency of 500 kHz we have observed a single compressional wave in the former whose speed is 1.79 km/s and two distinct compressional waves with speeds 2.81 km/s and 0.96 km/s in the latter. The Biot theory is shown to give an accurate description of this phenomenon. We also analyze the acoustics of low temperature He ii in packed powder superleaks; either the fast wave for unconsolidated systems or the slow wave in a highly consolidated (fused) frame may be considered to be the 4th sound mode. In all such systems, the acoustic properties can be very simply understood by considering the velocities of propagation as continuous functions of the elastic moduli of the solid skeletal frames.

An ultrasonic pulse technique has been developed for measuring phase velocity and attenuation spectra in rocks inside a pressure vessel. This technique has been adapted from those used in the nondestructive evaluation field. In essence, a broadband acoustic pulse is directed into a lucite buffer, which is followed by the rock sample and another lucite buffer. The pulse partially reflects off both the front and back faces of the sample, and the reflected pulses are received by the transmitting transducer. Digital recording and signal processing techniques are used to analyze the signal. After Fourier transforming each pulse, correcting for diffraction effects, and allowing for partial reflections at the interfaces, the phase shift between pulses at each frequency yields the phase velocity and the amplitude reduction gives the attenuation. Tests on synthetic materials show that as currently implemented, the technique produces reliable measurements at frequencies above 400 kHz. Velocity and attenuation spectra are shown for brine saturated Massilon and Boise sandstones at different effective pressures.

The ultrasonic properties (reflection/transmission and bulk attenuation/speed) of porous and permeable media saturated with a Newtonian fluid, namely water, are considered. The frequency dependence of the transmission amplitudes of pulses is measured through a slab of thickness d1, repeated for another slab of thickness d2 for a given material. With these two measurements on two different thicknesses, it is possible in principle to separate bulk losses from reflection/transmission losses for compressional waves in these materials. The bulk properties are calculated from the Biot theory for which all of the input parameters have been measured separately; the attenuations are particularly sensitive to the values of Λ, determined from second-sound attenuation measurements reported in the companion article. There is excellent quantitative agreement between the theoretical and experimental values in the cases considered; there are no adjustable parameters involved. The reflection and transmission coefficients are reported for some of the multiply reflected pulses and their amplitudes are compared with those calculated from the Deresiewicz–Skalak and Rosenbaum boundary conditions appropriate to either the open-pore or sealed-pore surfaces, as the case may be. Again, there is excellent quantitative agreement between theory and experiment. Compared with the open-pore boundary conditions, it is noted that there is a large reduction, both theoretically and experimentally, in the efficiency with which the slow compressional wave is generated when the sealed-pore boundary conditions apply, but this efficiency is not reduced to zero.