## 1 Introduction  
Granular materials can be used to form thin and lightweight sound-absorbing layers, which have multiple useful applications. General granular materials with grain diameters of a few millimeters exhibit acoustic properties similar to those of porous materials, where the kinetic energy of sound waves is converted into thermal energy by the boundary layer viscosity of air near the material walls, resulting in sound absorption [1]. For granular materials consisting of several millimeters in grain size, multiple theoretical analysis methods are available for estimating the sound absorption coefficient of granular materials with grain sizes of a few millimeters for both regular filling structures [2] and random filling structures [3]. For the acoustic properties of granular materials several studies have been conducted: a study comparing the accuracy of the application of three general porous prediction models [4]; a study of the relationship between sound velocity in a mixture of granular materials and the composition of the mixture [5]; a study that devised a new empirical model for the acoustic properties of loose granular media [6]; and a study that carried out an inverse estimation of non-acoustic parameters for granular absorbers and a comparison of impedance models [7]. Research on sound absorbers using granular materials includes studies on a new system of thin impermeable circular membranes made of silicone lined with cavities partially filled with granular AC [8] and the development of natural fiber-grain composites as new sustainable sound-absorbing materials made of kenaf fibers and waste rice husk grains [9]. Research has also been carried out on the use of granular materials as sound insulation materials, such as the measurement of the transmission loss in regenerated granular materials using wave decomposition with deconvolution-based impulse response extraction [10]. Research has reported examples of the measured insertion loss of wedge-shaped barriers with sand and gravel and calculations performed using empirical models [11]. At low frequencies, a high sound absorption coefficient can be obtained by using powder materials with much smaller grain sizes of several tens of micrometers. [PERSON] et al. [12] explained the sound absorption mechanism of powder materials as follows: a sound wave excites the longitudinal vibration modes of the powder grains, which converts the acoustic energy into kinetic energy that is attenuated by the interaction between powder grains. Research involving powder materials includes studies on the effects of grain size on the sound absorption properties and sound velocity of powder layers [13], the acoustic behavior of powder layers comprising two different powder mixtures [14], the sound absorption properties of materials consisting of polymer grains and polyurethane foam [15], and sound absorption in aerogel powders saturated in air [16]. The acoustic behavior of the powder layer is sometimes analyzed using the Biot model [17], including studies on the influence of casing on the sound absorption properties of fine spherical granular materials [18]. [PERSON] et al. [19] estimated the sound absorption coefficient of a powder layer by treating it as a five-degrees-of-freedom forced vibration problem and calculating the acoustic impedance derived from the equation of motion. For powders with a relatively large grain size, high bulk density, or both, vibration analysis alone does not provide a sufficient calculation accuracy. Thus, [PERSON] et al. [20] derived the sound absorption coefficient of a powder layer by modeling both the longitudinal vibration of the powder and damping due to the viscosity of the boundary layer. [PERSON] et al. [21] showed that there is no clear correlation between the grain size and first sound absorption peak. They did find that a lower bulk density correlated with a higher sound absorption coefficient.