Fig 2. Approximation to the scattering beampattern of a disc.

A) evaluation of the truncated infinite series for the leaf beampattern coefficient (Eq 2) and its approximation using a cosine function; solid line: series evaluation; dashed line: cosine fit (acos(bθ₀)). The result from the infinite series and the cosine approximation are shown as a function of incident angle θ₀ (0° to 90°) for the case of kr = 14, where k is wave number and r is the leaf radius. B) and C) Fitting curves used to determine the amplitude a and angular frequency b of the cosine fit as a function of kr. Open circles: parameter values determined from evaluating a truncated version of the infinite series; solid lines: curve fitted to the data points marked with the open circles.