Singing sands, booming dune sands, and the stick–slip effect

Abstract

The origin of the acoustic and seismic emissions from impacted singing grains and from avalanching dune sand grains is sought in modes of vibration in discreet grain columns. It is postulated that when the grains in a column are pressed together and forced to slide over one another, elastic shear bands are formed at the contact areas with distinct elastic moduli. Such contact shear bands would have implications in the formulation of the Hertz–Mindlin contact theory. The assembly of all grain columns below the impacting pestle forms the slip (slide) shear band. The transfer of energy from the pestle to the modes of vibration in such columns is effected by the stick–slip effect. The intense collective vibration of all columns in the slip shear band results in the familiar musical sound. The concept of grain flowability is used to justify the disparity between the acoustic emissions from impacted singing grains and from avalanching booming dune sand grains. The concept of grain columns is assumed to apply in the freely avalanching sand band, but with longer length to justify the lower frequencies. This approach predicts frequency spectra comprising a low-frequency content and a dominant frequency with its harmonics in agreement with the experimental evidence. Additionally, it can account for the low-frequency vibration evoked when booming sand flows through a funnel, with implications in the understanding of grain silo vibrations. It is argued that sand grains do not sing or boom because the stick–slip effect in not applicable in the contact shear bands.