Approved for public release; distribution is unlimited / Reissued 30 May 2017 with Second Reader’s non-NPS affiliation added to title page. / The scalar reciprocity equation commonly stated in underwater acoustics relates pressure fields and monopole sources. It is often used to predict the pressure measured by a hydrophone for multiple source locations by placing a source at the hydrophone location and calculating the field everywhere for that source. That method, however, does not work when calculating the orthogonal components of the velocity field measured by a fixed receiver. This thesis derives a vector-scalar reciprocity equation that accounts for both monopole and dipole sources. This equation can be used to calculate individual components of the received vector field by altering the source type used in the propagation calculation. This enables a propagation model to calculate the received vector field components for an arbitrary number of source locations with a single model run for each received field component instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic solutions for a range-independent environment and with numerical solutions for a range-independent and a range-dependent environment using a parabolic equation model. / Electronics Engineer, Naval Undersea Warfare Center

The concept of a weak sound radiating cell is proposed to reduce the low frequency radiated noise from structures. The cell consists of two coupled surfaces such that, when placed on a vibrating structure, the responses of the two surfaces are nearly out-of-phase and of equal strength over a wide frequency range. This structure response leads the cell to behave as an acoustic dipole and thus as a poor sound radiating source. The control of low frequency structurally radiated noise is then achieved by covering the structure with an array of these weak radiating cells, i.e. surface treatment. Thus, the surface treatment essentially transforms the response of the structure to that of a distributed array of dipoles yielding a low sound radiating structure. Theoretical models are developed to predict the performance of the cell. Experimental verification is performed for a single cell applied to a piston-like structure to demonstrate the concept on a simple radiating structure. The results demonstrated an overall sound power level reduction of 5.2 dB between 400-1600 Hz with maximum reductions over 30 dB at discrete frequencies. Finally, an array of weak radiating cells is experimentally applied to a more complex structure, a rectangular plate. The results of the plate experiments reveal an overall sound power level reduction of 10.2 dB between 100-1600 Hz with maximum reductions of 25 dB at discrete frequencies. These results demonstrate the potential of the weak radiating cell concept to reduce low frequency structurally radiated noise. / Master of Science