# Experimental Analysis of Ultrasonic Multiple Scattering Attenuation through the Air with Fine Dust
## 1 Introduction  
Fine dust particles in the air, such as particulate matter, have been a serious societal challenge worldwide [1, 2, 3]. [PERSON] et al. investigated the composite of dust in India [1] while [PERSON] et al. and [PERSON] discussed a removal methodology in China and the United States [2, 3]. Airborne fine dust is a critical environmental issue and a potential threat to human health [4]. In particular, the heavy density of fine dust in the air causes secondary indoor air pollution in urban areas because people avoid natural ventilation via fresh air. Therefore, the accurate measurement of fine dust concentration is essential for human health. Currently, the proposed techniques for measuring the concentration of fine dust include the beta ray, gravimetric, light scattering, and semiconductor-based gas sensor methods [5]. The beta line and gravimetric methods, which have relatively high accuracy, are not suitable for real-time data collection because they require the collection time of fine dust for a certain period [6, 7]. The most widely used light scattering method is based on the light source phenomenon, where laser is scattered proportionally to the concentration of fine dust [8]. The gas sensor is based on the contraction and expansion effect, as well as the change in electrical resistance triggered by adsorption and desorption when fine dust contacts the surface of the semiconductor. Although light scattering and gas sensors that provide fast data at relatively low prices have been widely applied in the field, they are susceptible to environmental factors such as relative humidity; hence the need for additional calibration procedures [9, 10, 11]. Mechanical waves can be applied to the measurement of dust particles, where the wave propagation is less susceptible to changes in relative humidity. Ultrasound has been employed to estimate dust concentration in various industrial fields. [PERSON] et al. evaluated the aluminum dust concentration in a spherical vessel [12] while [PERSON] et al. monitored the dust concentration in a powder classifier [13]. A recent study conducted by the authorsproposed a fine dust measurement method based on the independent scattering approximation theory and verified its effectiveness via numerical simulation [14]. The number of fine dust particles per unit area, called the number density, is directly computed by the scattering wavefield without additional calibration. The proposed theory numerically evaluated that the attenuation of coherent waves over the frequency corresponds well with the number density under a low volume fraction of the fine dust in air (below 2%). In this study, the ultrasonic multiple scattering method for estimating the number density was experimentally verified. A series of ultrasonic experiments were performed with and without a controlled environment. The number density of fine dust particles was calculated using the measured ultrasonic data based on the independent scattering approximation theory. The signal processing procedure was also suggested by considering a three-dimensional wave propagation, such as geometric spreading. The unique contributions of this study are summarized as follows: (1) it provides the first experimental validation for the measurement of fine dust in air using mechanical wave scattering, (2) it develops an ultrasonic multiple scattering hardware that measures the attenuation of propagating waves in linear space, and (3) it develops a signal processing procedure that calculates ultrasonic scattering attenuation triggered by fine dust in air using the proposed ultrasonic scattering method. The structure of this article includes a theoretical background on multiple scattering of acoustic waves in randomly distributed particles through the medium in Section 2, signal processing in Section 3, experimental details in Section 4, and experimental results and discussion in Sections 5 and 6, respectively.