In this paper, we show how appropriate superpositions of Bessel beams can be successfully used to obtain arbitrary longitudinal intensity patterns of nondiffracting ultrasonic wave fields with very high transverse localization. More precisely, the method here described allows generation of longitudinal acoustic pressure fields whose longitudinal intensity patterns can assume, in principle, any desired shape within a freely chosen interval 0 ≤ z ≤ L of the propagation axis, and that can be endowed in particular with a static envelope (within which only the carrier wave propagates). Indeed, it is here demonstrated by computer evaluations that these very special beams of nonattenuated ultrasonic field can be generated in water-like media by means of annular transducers. Such fields at rest have been called by us acoustic frozen waves (FWs). The paper presents various cases of FWs in water, and investigates their aperture characteristics, such as minimum required size and ring dimensioning, as well as the influence they have on the proper generation of the desired FW patterns. The FWs are particular localized solutions to the wave equation that can be used in many applications, such as new kinds of devices, e.g., acoustic tweezers or scalpels, and especially in various ultrasound medical apparatus.