A model for near-perfect transmission through lossy media with acoustic sources

Acoustic metamaterials exhibit effective material properties not found in naturally occurring media, and, as such, have received considerable attention for their potential applications in noise and vibration control, diagnostic imaging, and nonreciprocal transmission. Complementary acoustic metamaterials have been proposed as a means of compensating for the high impedance mismatches of aberrating layers that disrupt the acoustic field and hence distort acoustic images. More recently, a complementary acoustic metamaterial featuring active components was shown in principal to compensate for both the impedance mismatch and energy attenuation of lossy materials, but a physical realization of the concept has not yet been implemented. Here, we present results from a one-dimensional acoustic model showing how a plane wave incident on a lossy material can be augmented by point monopole and dipole sources to allow for near perfect transmission, thus rendering the lossy medium acoustically transparent. We present general expressions for source magnitudes that are dimensionless with respect to frequency, material thickness, and the background medium. We show that these results are consistent with three-dimensional finite element simulations, where the appropriate monopolar and dipolar forces are generated using finite dimensional velocity sources with real loudspeaker characteristics mounted in an acoustic waveguide.