An analytic study of high-frequency sound field reproduction using active control methods

Sound field reproduction through active control measures provides a means to mitigate, or “cancel,” a scattered acoustic field from an ensonified object. This concept is studied for acoustic cloaking of a rigid sphere to assess the number of control sources and error sensors necessary to achieve significant high-frequency scattered field attenuation. This study expands upon previous work by Cheer [Cheer, J. Acoust. Soc. Am. 140 1502–1512 (2016)] which explored active control techniques for simplistic scattering geometries relegated to ka numbers below four using finite element method. This work extends the prior study to ka numbers greater than 16 by instead leveraging canonical analytic solutions to calculate the scattered and radiated pressure fields. This approach overcomes computational limitations in high-frequency finite element methods and allows for the study of multiple control source geometries and variable error sensor densities. At high ka numbers, scattered field attenuation metrics are presented, which indicate impracticability of an isotropic acoustic cloaking solution, even for idealized scattering geometries. Further commentary on achieving realistic implementation is provided within the limitations of sensor element count and reproduced sound field frequency.