Redirection and Splitting of Sound Waves by a Periodic Chain of Thin Perforated Cylindrical Shells

Abstract

The manipulation of $l\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}g\phantom{\rule{0}{0ex}}h\phantom{\rule{0}{0ex}}t$ via engineered structures (metamaterials) continues to inform the manipulation of $s\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}d$. The authors show analytically that a periodic chain of perforated metallic shells can transform an audible sound of wide frequency spectrum into two monochromatic waves that propagate along the chain in opposite directions. Such a chain may serve not only as a splitter and redirector of acoustic waves, but also as a passive antenna that points the way back to the source of the incoming sound.