In this paper, we develop a tractable mathematical model and emulation framework for communicating information through water using acoustic signals. Water is considered as one of the most complex mediums to model owing to its vastness and variety in characteristics depending on the scenario, what kind of water-body (lakes, rivers, tanks, sea etc.) and geographical location of the water-body is considered. Our proposed mathematical model involves the concept of damped harmonic oscillators to represent the medium (water) and Milne’s oscillator technique to map the interaction between the acoustic signal and water. Wave equations formulated for acoustic pressure and acoustic wave velocity are used to characterize the travelling acoustic signal. Signal strength, phase shift and time-delay generated from the mathematical model are fed to a Simulink-based emulator framework to generate channel samples and channel impulse responses. The emulator uses wide sense stationary uncorrelated scattering (WSSUS) assumption and finite sum-of-sinusoids (SOS) with uniformly distributed phase to generate the channel samples. Using the emulator platform it is possible to generate amplitude variation profile, Doppler shift and spread experienced by any travelling signal through different underwater communication scenarios. Such an emulator platform can be used to simulate different communication scenarios, underwater network topologies, data to train different learning models and predict performance of different modulation, multiplexing, error correction and multi-access techniques for underwater acoustic communications (UWAC) systems.