  A rigorous reduction of the many-body wave scattering problem to solving a
linear algebraic system is given bypassing solving the usual system of integral
equation. The limiting case of infinitely many small particles embedded into a
medium is considered and the limiting equation for the field in the medium is
derived. The impedance boundary conditions are imposed on the boundaries of
small bodies. The case of Neumann boundary conditions (acoustically hard
particles) is also considered. Applications to creating materials with a
desired refraction coefficient are given. It is proved that by embedding
suitable number of small particles per unit volume of the original material
with suitable boundary impedances one can create a new material with any
desired refraction coefficient. The governing equation is a scalar Helmholtz
equation, which one obtains by Fourier transforming the wave equation.
