The production of acoustic signals from the interactions of ultra-high energy (UHE) cosmic ray neutrinos in water and ice has been studied. A new computationally fast and efficient method of deriving the signal is presented. This method allows the implementation of up to date parameterisations of acoustic attenuation in sea water and ice that now includes the effects of complex attenuation, where appropriate. The methods presented here have been used to compute and study the properties of the acoustic signals which would be expected from such interactions. A matrix method of parameterising the signals, which includes the expected fluctuations, is also presented. These methods are used to generate the expected signals that would be detected in acoustic UHE neutrino telescopes.
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