  This paper concerns mathematical formulation of well-known MUltiple SIgnal
Classification (MUSIC)-type imaging functional in the inverse scattering
problem by an open sound-hard arc. Based on the physical factorization of
so-called Multi-Static Response (MSR) matrix and the structure of left-singular
vectors liked to the non-zero singular values of MSR matrix, we construct a
relationship between imaging functional and Bessel function of order $1$ of the
first kind. We then expound certain properties of MUSIC and present numerical
results for a number of differently chosen smooth arcs.
