  This article presents an error analysis of the symmetric linear/bilinear
partially penalized immersed finite element (PPIFE) methods for interface
problems of Helmholtz equations. Under the assumption that the exact solution
possesses a usual piecewise $H^2$ regularity, the optimal error bounds for the
PPIFE solutions are derived in an energy norm and the usual $L^2$ norm provided
that the mesh size is sufficiently small. A numerical example is conducted to
validate the theoretical conclusions.
