In a wedge shaped ocean, the method of images is used to develop an analytical approximation of the acoustic pressure field. Contemporary work develops acoustic doublets from a combination of the source and surface reflection image using simple dipole theory. The method of images is then used to sum the dipole images. This thesis matches dipole pairs to achieve a quadruplet expansion. A computer program using the derived quadruplet equation is then created to verify the results by comparing them with the URTEXT program. Method of images, Quadruplet expansion.