An expression is obtained for the amplitude and phase of an acoustic wave above a boundary due to a point source on or near a boundary which exhibits a constant normal specific acoustic impedance. This is shown to be a special case of the solution for an isotropic medium with constant characteristic acoustic impedance; specifically, the case is one in which the ratio of the propagation constant in the upper medium to that in the lower approaches 0.A material which obeyed a constant normal impedance boundary condition was constructed from ordinary drinking straws. Measurements of amplitude and phase as a function of receiver position along and above the boundary showed good agreement with theory.The nature of the approximations involved in the solution are discussed and it is shown to be an adequate representation of the sound field for distances greater than one wavelength from the source.