The method of Cagniard is employed to obtain an exact solution for the pressure response to a spherically symmetric acoustic pulse originating at a source within a semi-infinite fluid bounded below by a fluid of higher sound velocity. The solution is expressed in terms of elliptic integrals. The shape of that portion of the response known as the refracted arrival is shown to depend principally upon the density contrast. The response is plotted as a function of time for parameters which represent the reflection process from the ocean bottom. If the pulse from the source has a steep initial rise time, then reflection at angles greater than the critical angle may lead to unexpectedly large amplitudes for a brief time interval. It is suggested that this phenomenon may introduce nonlinear effects into the reflection process.