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Underwater acoustic communications in the ocean is complicated as the acoustic signals may be attenuated, distorted and delayed. In this paper, we review the underwater acoustic signal propagation properties in terms of sound speed profile, spreading loss and absorption loss. We study and compare different approaches on the calculation of signal transmission loss in the water, more specifically, the ray theory model approach and the semi-empirical formula approach. Using the Acoustic Toolbox, we compare their performance under different environmental parameters, including the sound source depth, bathymetry data, and the horizontal distance between the sound source and receiver. Furthermore, in order to obtain how the acoustic propagation characteristics will affect the performance of medium access control (MAC) protocol, we adopt pure ALOHA protocol and use network simulator ns-2 to study the throughput performance under both shallow water and deep ocean conditions. Our results indicate that the transmission loss in the shallow water is close to the result of semi-empirical formula with transition region (k = 1.5), which is close to the result of semi-empirical formula with spherical spreading loss (k=2) in deep water.