In apparatus for the acoustic transmission of power or data through a solid barrier such as a ships hull, assembly of an acoustic transducer to the hull is facilitated by bonding it first to an intermediate element by a thin layer of bonding adhesive and then bonding the intermediate element to the barrier using a second bonding layer. Acoustic matching of the transducer to the intermediate element is achieved by the thin layer, and the mechanically more robust base of the intermediate element can be rubbed on the barrier surface to displace or abrade away any unwanted debris or imperfections which might otherwise prevent the achievement of a thin second bonding layer. This makes the mounting and bonding process more tolerant of imperfections in the barrier surface due to either surface defects or particulate contamination. The transmit and receive transducers may be positioned relative to each other so as to suppress or attenuate multiple-transit signals. Thus the intermediate element may be wedge shaped to aid suppression of triple-transit signals. Transmit and receive transducers may have different wedge angles.