# Acoustic Pressure Amplification through In-Duct Sonic Black Holes
## 1 Introduction  
An increasing awareness has appeared in the last few years concerning energy efficiency in the development of sustainable buildings [1]. Modern construction is built considering stricter insulation standards to ensure high energy savings [2], which can also imply poor indoor air quality. Ventilation systems are thus essential for the health and comfort of building occupants [3]. They play a central role in ensuring not only adequate levels of temperature and humidity but also a good quality of indoor air. Additionally, airborne transmission and concentration of bacteria and viruses are directly influenced by adequate airflow, contributing to a healthier built environment [4]. Failures of indoor building ventilation systems that are not fixed at an early stage lead to more expensive repairs or even to compressor failures and the need to replace the entire system [5]. Early problem identification is made through assessment and diagnosis procedures that comprise different techniques. Most common solutions use duct measurements to perform air flow monitoring using audio sensing techniques [6; 7; 8]. Many of these recent applications have developed distributed acoustic sensor systems using machine learning algorithms deployed on smartphones. The real-time monitoring of ventilation systems isable to classify and detect failures at an early stage. However, these sensor systems can be expensive for implementation and maintenance upgrades. In addition, they present the intrinsic limitation of the minimum detectable pressure, which can be masked due to the presence of high background noise. The pressure limit detection problem also appears in other areas concerning transmission data in communications, with challenges of noise and attenuation affecting the integrity of the signal [9], structural monitoring and rehabilitation of in-service structures due to the sensitivity of the measured parameters with respect to the intensity of the change [10], or medical image analysis for proper interpretation of noisy image data [11]. Additional solutions to enhance the sensing of weak signals are of fundamental importance in these areas. In recent decades, the development of acoustic metamaterials has brought new perspectives for manipulating sound waves [12]. They are engineered materials with designed internal structures and geometries used to induce effective properties that are substantially different from those found in their components alone. This is accomplished by exploiting subwavelength micro-structures embedded in a background medium. The response of properly defined unit cells can be translated into averaged effective parameters, namely an effective density and bulk modulus [13]. The objective is to create a structural building block that, when assembled into a larger sample, exhibits the desired values of these key effective parameters. A review of several applications can be found in [13]. Metamaterials have been considered in the field of acoustic sensing for the amplification of acoustic pulse signals hidden by background noise. [PERSON] et al. [14] have proposed an anisotropic acoustic metamaterial made up of graded cavity depths that compressed the sound wavelength and enabled the spatial concentration of the acoustic energy and the amplification of the signal. The concept was validated using a design composed of alternative layers of metal with air gaps of increasing widths. The experiments were performed in anechoic conditions. It proved the phenomenon of wave compression at 7 kHz and pressure amplification of more than 20 dB compared to that obtained without the metamaterial. The same configuration has been revisited more recently [15], including gradient-coiling metamaterials to lower the operational frequency of detection. The structure was composed of 24 rectangular plates with a nonlinear profile varying along the wave propagation direction, with curved cells between the slits. The proposed configuration was 3D printed and tested in response to various pulse signals generated by a loudspeaker.