New physical aspects of collinear acousto-optical interaction, occurred by acoustic waves of finite amplitude, are revealed and analyzed in crystalline materials exhibiting moderate linear acoustic losses. The analysis is performed in the regime of continuous traveling waves allowing specific mechanism of the acousto-optic nonlinearity. Our consideration has shown that such nonlinearity together with linear acoustic losses is able to affect the transmission function inherent in collinear interaction. In particular, the mere presence of linear acoustic losses by themselves leads to broadening the width of transmission function beginning already from very low levels of the applied acoustic power. Moreover, the transmission function exhibits a marked and quasi-periodical dependence on the applied acoustic power density; and that periodicity is governed by the linear acoustic losses. As a result, the transmission function can be significantly narrowed near isolated points at the cost of decreasing the interaction efficiency. These novelties related to collinear acousto-optical interaction accompanied by moderate linear acoustic losses have been studied and confirmed experimentally with an advanced acousto-optical cell based on calcium molybdate (CaMoO4 ) single crystal and controlled by acoustic waves of finite amplitude.