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We report an experimental and theoretical investigation of thefrequency-dependent effective mass, $\tilde{M}(\omega)$, of loose granularparticles which occupy a rigid cavity to a given filling fraction, theremaining volume being air of differing humidities. This allow us to study themechanisms of elastic response and attenuation of acoustic modes in granularmedia. We demonstrate that this is a sensitive and direct way to measure thoseproperties of the granular medium that are the cause of the changes in acousticproperties of structures containing grain-filled cavities. Specifically, weapply this understanding to the case of the flexural resonances of arectangular bar with a grain-filled cavity within it. The dominant features of$\tilde{M}(\omega)$ are a sharp resonance and a broad background, which weanalyze within the context of simple models. We find that: a) These systems maybe understood in terms of a height-dependent and diameter-dependent effectivesound speed ($\sim 100-300$ m/s) and an effective viscosity ($\sim 5\times10^4$ Poise). b) There is a dynamic Janssen effect in the sense that, at anyfrequency, and depending on the method of sample preparation, approximatelyone-half of the effective mass is borne by the side walls of the cavity andone-half by the bottom. c) By performing experiments under varying humidityconditions we conclude that, on a fundamental level, damping of acoustic modesis dominated by adsorbed films of water at grain-grain contacts in ourexperiments, not by global viscous dampening. d) There is a monotonicallyincreasing effect of humidity on the dampening of the fundamental resonancewithin the granular medium which translates to a non-monotonic, butpredictable, variation of dampening within the grain-loaded bar.

Dynamic effective mass of granular media and the attenuation of structure-borne sound