Using a sonar in a different environment from that of its calibration: effects of changes in salinity and temperature

It is a universal truth that calibrating a sonar under the environmental conditions of its actual application is a desideratum. However, this is often inconvenient or impracticable. The problem thus arises of accounting for differences in environmental conditions between calibration, or other performance measurement, and application. Three particular environmental influences are salinity, temperature, and transducer depth, i.e., pressure. These largely determine the local mass density and sound speed in water. Two effects of changing environment on transducer performance are identified. (1) A change in medium sound speed affects the transducer beam pattern, thence the beamwidth and equivalent beam angle, namely the integral of the product of the transmit and receive beam patterns over all angles in the transducer farfields. (2) Changes in mass density and/or sound speed affect the acoustic particle velocity and pressure or stresses, thence the efficiency of transduction: (i) elastic-wave energy entering the water medium through the transducer-water interface, and (ii) acoustic-wave energy entering the transducer through the same interface. The first environmental effect was treated previously. The second effect is analyzed here for the single identified transducer material for which the temperature dependence of an elastic modulus is available, namely barium titanate, a ferroelectric electrostrictive material. The magnitude of the effect is estimated for a simple model over the temperature range [1,18]°C. While this second effect is particular to the material, the finding of an effect of similar magnitude argues for performance studies of transducers over a wider range of medium conditions than are ordinarily available but that are encountered in situ.