Back reflection of acoustic waves by a 1-D rigid panel with periodically embedded Helmholtz resonators

Reflection of an obliquely incident plane acoustic wave by a rigid boundary that is periodically embedded with Helmholtz resonators is investigated.The resonator spacing d and the incident wavelengthλare assumed of the same order,both longer than the dimension of each Helmholtz resonator.Both analysis and computation show that for an incident acoustic wave with a frequency satisfying both conditions for the Bragg resonance and the Helmholtz resonance,the reflected wave disappears in the usual direction of reflection,but appears in the direction opposite to the incidence.The phenomenon is referred to in this work as back reflection,a new type of reflection completely different from the usual one.