  We demonstrate both numerically and experimentally that geometric frustration
in two-dimensional periodic acoustic networks consisting of arrays of narrow
air channels can be harnessed to form band gaps (ranges of frequency in which
the waves cannot propagate in any direction through the system). While resonant
standing wave modes and interferences are ubiquitous in all the analyzed
network geometries, we show that they give rise to band gaps only in the
geometrically frustrated ones (i.e. those comprising of triangles and
pentagons). Our results not only reveal a new mechanism based on geometric
frustration to suppress the propagation of pressure waves in specific frequency
ranges, but also opens avenues for the design of a new generation of smart
systems that control and manipulate sound and vibrations.
