There is a reference to sound mirrors (and this website!) in the University of Florida’s Journal of Undergraduate Research, Volume 9, Issue 2. November/December 2007.
Nikolas Zawodny’s paper on the Design and Fabrication of a Phased Acoustic Array to Analyze Noise Generation of Aircraft Components does what it says on the tin, though there appears to be lots of hard sums involved.
Early techniques of airframe noise analysis involved the concept of an “acoustic mirror,” which consisted of a single microphone positioned in the acoustic far field of a large concave elliptical mirror. The origin of acoustic mirrors can be traced back to the north and southeast coasts of England in the early 1920s, where they were used to provide early warning of incoming enemy aircraft planning to attack coastal towns. These coastal “listening ears” were eventually rendered obsolete with the development of faster aircraft and the invention of radar.
The date is actually slightly out, as some mirrors were built during World War I.