  It is proved that the set of scattering amplitudes $\{A(\beta, \alpha,
k)\}_{\forall \alpha \in S^2}$, known for all $\beta\in S^2$, where $S^2$ is
the unit sphere in $\mathbb{R}^3$, $k>0$ is fixed, $k^2$ is not a Dirichlet
eigenvalue of the Laplacian in $D$, is dense in $L^2(S^2)$. Here $A(\beta,
\alpha, k)$ is the scattering amplitude corresponding to an obstacle $D$, where
$D\subset \mathbb{R}^3$ is a bounded domain with a boundary $S$.
  The boundary condition on $S$ is the Dirichlet condition.
