  The model problem of scattering of a sound wave by an infinite plane
structure formed by a semi-infinite acoustically hard screen and a
semi-infinite sandwich panel perforated from one side and covered by a membrane
from the other is exactly solved. The model is governed by two Helmholtz
equations for the velocity potentials in the upper and lower half-planes
coupled by the Leppington effective boundary condition and the equation of
vibration of a membrane in a fluid. Two methods of solution are proposed and
discussed. Both methods reduce the problem to an order-2 vector Riemann-Hilbert
problem. The matrix coefficients have different entries, have the
Chebotarev-Khrapkov structure and share the same order-4 characteristic
polynomial. Exact Wiener-Hopf matrix factorization requires solving a scalar
Riemann-Hilbert on an elliptic surface and the associated genus-1 Jacobi
inversion problem solved in terms of the associated Riemann $\theta$-function.
Numerical results for the absolute value of the total velocity potentials are
reported and discussed.
