  The governing equation is $[\nabla^2+k^2-q(x)]u=0$ in $\R^3$. It is shown
that any desired potential $q(x)$, vanishing outside a bounded domain $D$, can
be obtained if one embeds into D many small scatterers $q_m(x)$, vanishing
outside balls $B_m:=\{x: |x-x_m|<a\}$, such that $q_m=A_m$ in $B_m$, $q_m=0$
outside $B_m$, $1\leq m \leq M$, $M=M(a)$. It is proved that if the number of
small scatterers in any subdomain $\Delta$ is defined as
$N(\Delta):=\sum_{x_m\in \Delta}1$ and is given by the formula
$N(\Delta)=|V(a)|^{-1}\int_{\Delta}n(x)dx [1+o(1)]$ as $a\to 0$, where
$V(a)=4\pi a^3/3$, then the limit of the function $u_{M}(x)$, $\lim_{a\to
0}U_M=u_e(x)$ does exist and solves the equation $[\nabla^2+k^2-q(x)]u=0$ in
$\R^3$, where $q(x)=n(x)A(x)$,and $A(x_m)=A_m$. The total number $M$ of small
inhomogeneities is equal to $N(D)$ and is of the order $O(a^{-3})$ as $a\to 0$.
  A similar result is derived in the one-dimensional case.
