Reflection and Scattering of Acoustical Waves from a Discontinuity in Absorption

The reflection and transmission of a plane acoustical wave from a planar boundary at the interface between two homogeneous media of different acoustical properties is a classical problem in acoustics that has served as a basis for many developments in acoustics for over 100 years. This problem, detailed in virtually every textbook on acoustics, provides us with the acoustical analogue to Snell’s Law in optics and gives us correspondingly simple results. Classical acoustics predicts that a reflection from a boundary occurs only if the characteristic acoustical impedances of the two media are different. Here we show that a reflection also occurs if the media have the same impedances but different absorption coefficients. Our analysis yields some surprising results. For example, a reflection will occur at a discontinuity in absorption even if the impedance is uniform and continuous across the interface. In addition, a discontinuity in impedance at an interface between two media that have constant and equal, but non-zero absorption, results in a reflection coefficient that is dependent on absorption as well as impedance. In general, reflection coefficients now become frequency dependent. To experimentally test our results, we measured the reflection at the interface between water and castor oil, two liquids with similar impedances but very different absorption coefficients. Measurement of the reflection coefficient between 1 and 50 MHz demonstrated a frequency dependence that was in good agreement with our analysis.