  We consider the 2D acoustic system with the Gaussian pulse as the initial
data. This case was proposed at the first Workshop on benchmark problems in
computational aeroacoustics, and it is commonly used for the verification of
numerical methods. We construct an efficient algorithm to evaluate the exact
solution for a given time t and distance r. For a precision eps, it takes
c*ln(1/eps) operations (the evaluation of a Bessel function counts as one
operation) where c does not depend on t and r. This becomes possible by using
three different integral representations and an asymptotic series depending on
t and r.
