Acoustical interaction of spherical and cylindrical bubbles on plane sheets and ribbons

Theory is developed to describe the acoustical interaction of a plane wave with a ribbon of material containing resonant scatterers. Infinitely wide, finite and very narrow ribbons are considered which contain free spherical bubbles, plant-tissue gas bodies (cylindrical bubbles) or bubbles trapped in pores. The interaction leads to a reduction of the pressure amplitude at the bubbles below that of the normally-incident plane wave, and this reduces the resulting pulsation amplitude of the bubbles, especially at resonance. The results are applicable to quantitative studies of physical, chemical and biological effects of ultrasound when stable cavitation is important.