Line and plane arrays of resonant monopole scatterers

Arrays of n identical resonators (bubbles, gas‐filled balloons, and thin shells) in periodic arrays of spacing l and insonified by a plane wave at frequencies near the monopole resonance (bubble) frequency ω₀ display strong resonances due to multiple scatter interaction. One‐dimensional systems (linear arrays) in full spaces exhibit pronounced partial resonances (quasiresonances or QRs), for both finite and infinite n, with absolute magnification of the free‐field amplitude (i.e., in the absence of the system) of up to 7×10² inside or on the surface of each resonator. These QR effects have strong directionality: The amplitude response of each scatterer may vary by a factor of about 200, depending upon the direction of arrival of the insonifying plane wave. Of some general interest are the infinite line and plane arrays of the kind discussed by Weston [D. E. Weston, J. Acoust. Soc. Am. 39, 316–322 (1967)], for which we provide an improved treatment using exact estimates of multiple scatter interaction, as a result of which strong new resonances (QRs) are predicted under some conditions.