Measurement of dispersion and attenuation in granular media using a filter-correlation method

Abstract

A wideband technique for measuring sound dispersion and frequency-dependent attenuation in granular media is presented. The measurements were done on a mono-disperse medium of 2-cm solid polypropylene balls, over the frequency range of 500 Hz–20 kHz, enough to cover both weak- and strong-scattering regimes. A horn driver was used to launch sound into a foam-lined bucket containing the granular medium. The latter was mechanically isolated from the driver so as to minimize direct-contact coupling. The foam isolation was not enough, especially at resonances of the bucket-granular system. To account for the mass loading of the bucket by the granulars, the response of the bucket wall was measured by laser Doppler vibrometry both without and with the granulars. The response of the granular medium itself was extracted from the overall response through successive measurements of the individual responses of the driver, driver + bucket, and driver + bucket + granular. The frequency-dependent wavenumber of the granular is obtained by a filter-correlation method, using the driver response as reference. After successive bandpass filtering, the phase speed and attenuation are obtained within each band, respectively, by signal alignment and amplitude log ratio.