# A Multi-Tone Sound Absorber Based on an Array of Shunted Loudspeakers
## 1 Introduction  
The shunted loudspeaker, which consists of a closed-box loudspeaker and a shunt circuit, was first proposed for resonant acoustic field control in 2007 [1]. The acoustic impedance at the loudspeaker diaphragm and the resulting sound absorption coefficient can be adjusted by alternating the electric parameters in the shunt circuit, so the shunted loudspeaker can be implemented for noise control especially at low frequencies [2; 3; 4].  
Early studies on the shunted loudspeaker mainly focus on normal sound absorption performance. [PERSON] et al. studied the effect of the shunt circuit on the sound reflecting performance of a shunted loudspeaker in an impedance duct [2]. [PERSON] et al. employed the negative impedance converter to counter the D.C. resistance and voice coil inductance of the loudspeaker to broaden the sound absorption bandwidth [5]. [PERSON] et al. proposed constituting a thin compound broadband absorber by placing the shunted loudspeaker at the back of a micro-perforated panel [6]. [PERSON] et al. designed a shunt speaker with a sound absorption coefficient above 0.9 at both 100 Hz and 200 Hz to control the noise of the power transformer [7]. [PERSON] et al. replaced the closed box with a vented enclosure to enhance the sound absorption performance at low frequency [8]. [PERSON] et al. adopted the response surface method to optimize the parameters of the shunted loudspeaker (such as the moving mass, the enclosure volume, the filling density of mineral fiber, and the electrical load value) [9]. In the studies above, analog components were used in the shunt circuit, and it was difficult to adjust the electrical impedance precisely. [PERSON] et al. employed the real-time field programmable gate arraymodule and the voltage-controlled current source to constitute the shunt circuits [10]. [PERSON] et al. proposed a hybrid impedance control architecture for an electroacoustic absorber that combines a microphone-based feedforward control with a current driven electro dynamic loudspeaker system [11]. Considering the resonance characteristics of the mechanical system of the loudspeaker, the shunted loudspeaker is a typical resonant sound absorber with adjustable feedback impedance [12; 13; 14].  
For implementation, the performance of the array of shunted loudspeakers needs to be further investigated. A linear array of 10 shunted loudspeakers was placed in the reverberant chamber, and a sound pressure attenuation of 14 dB was achieved at 34.9 Hz [15]. Four shunted loudspeakers with surface area of 0.05 m\({}^{2}\) were placed in the corners of the rectangular room with dimensions of \(3\times 5.6\times 3.53\) m\({}^{3}\) to reduce the sound pressure level between 70 Hz and 100 Hz [16]. Thirty \(50\times 50\) mm shunted loudspeaker cells were assembled as liners inside a pipeline with air flow, and the obtained insertion loss was 16 dB at the target frequency [17]. A surface array of shunted loudspeakers could control the refracted direction of the incident sound around 350 Hz [18]. However, the sound absorption performance of the surface array of shunted loudspeakers has not been investigated.  
In this paper, a modal expansion method is proposed to calculate the normal sound absorption coefficient of the array of shunted loudspeakers with different acoustic impedances. The finite element model is further employed to validate the accuracy of the proposed method. Simulations show that each shunted loudspeaker can work almost independently. An experiment was conducted in the impedance duct with four different shunted loudspeakers to validate the feasibility of achieving multi-tone sound absorption.