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Abstract The forward problem arising in several hybrid imaging modalities can be modeled by the Cauchy problem for the free space wave equation. Solution to this problems describes propagation of a pressure wave, generated by a source supported inside unit sphereS. The datagrepresent the time-dependent values of the pressure on the observation surfaceS. Finding initial pressureffrom the known values ofgconsitutes the inverse problem. The latter is also frequently formulated in terms of the spherical means offwith centers onS. Here we consider a problem of range description of the wave operator mappingfintog. Such a problem was considered before, with datagknown on time interval at least $[0,2]$(assuming the unit speed of sound). Range conditions were also found in terms of spherical means, with radii of integration spheres lying in the range $[0,2]$. However, such data are redundant. We present necessary and sufficient conditions for functiongto be in the range of the wave operator, forggiven on a half-time interval $[0,1]$. This also implies range conditions on spherical means measured for the radii in the range $[0,1]$.