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

Abstract

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, elastic shear bands are formed at the contact areas with distinct elastic properties. The central part of such contact shear bands, where the stress level is maximum, is partially fluidized, resulting in reduced elastic moduli. In a given column, the elastic moduli would assume the lowest values just below the impacting pestle and higher values further below.The assembly of all grain columns below the pestle forms the slip 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 dune sand grains. The concept of grain columns is assumed to apply in the freely avalanching booming sand band, but with larger 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. It is argued that sand grains do not sing or boom since the stick-slip effect in not applicable in the contact shear bands.

Sound mechanics from squeaky and booming dune sands

“…In the experimental results shown in Figs. 2, 4 and 6 in Patitsas [1], where 11, 16 and 25 mm steel spheres were dropped on the beach sand from the north shore of Lake Michigan from the relatively low heights H equal to 10 and 20 cm, f 2 % 2 f 1 and no excitation at the pestle frequency f p is present. Evidently, the low impact velocity resulted in low impact band length L and low sand mass m s and in m p =m s ) 1.…”

“…Similar spectra can be seen in Figs. 8 and 10 in Patitsas [1] where a hand held 1.5 cm diameter rod was pushed slowly into the sand bed. The same can be seen in Takahara [12] where the sand bed was struck by a large pestle.…”

“…In an earlier report by Patitsas [1], it was argued that the origin of the acoustic emissions, when certain beach sands or other grains, such as silica gel grains, are stepped on or impacted by a pestle in a dish, can be found in the formation of elastic shear bands at the grain contact areas when the grains are subjected to compression and shear forces as can be seen in Fig. 1(a).…”

“…An appreciable amount of work on the acoustic emissions from dropping glass or steel spheres on a dish of squeaky grains can also be found in Patitsas [1]. However, the drop hight of the spheres was relatively low and the frequency shift of the harmonics was not observed.…”

“…The earlier work by Patitsas [1] lacked the concept of the ''collision shear band'' and the conclusions regarding the acoustic emissions when booming sand is pushed by a blade or allowed to avalanche freely are questionable. In this study, the collision shear band is assumed to be the source of the acoustic emission as are the contact shear bands in the case of the impacted sand.…”