Observation of the acoustic glory: High-frequency backscattering from an elastic sphere

Abstract

Measurements of the scattering of 2.10-MHz ultrasonic bursts gave direct evidence of the acoustic glory. Echo amplitudes were measured as a function of the transverse displacement x from the backward axis; they were maximized on the axis and they manifested side lobes. Except near minima, the amplitudes were proportional to J0(kbx/zn), where b and zn are the radius of, and axial distance to, the virtual focal circles from which the echoes appeared to emanate. This dependence on x is direct evidence of axial focusing. (The principal feature of optical glories of drops and bubbles is also axial focusing.) The experiment was performed in water with a fused silica sphere having a radius a≂51.6 mm for which 2πa/λ=ka≂457. A theory is developed for certain of the echo amplitudes and focal parameters. The theory typically overestimates the amplitudes of the stronger of the echoes by 5%. Appendices describe aspects of the theory not amenable to the experiment, including: (i) a shift of focal parameters which should be significant when ka≲100, and (ii) a distortion of transients described in part by the half-order derivative operator.