In acoustic underwater communication and sonar applications, obstacles inside and outside the line-of-sight (LOS) affect signal propagation. Both reflection and diffraction occur in underwater communication and measurement systems due to these obstacles. To the best of our knowledge, the influence of diffraction and reflection is neither described nor modeled for finite pulses yet. We propose and develop a multipath propagation model for spectral diffraction components and phase information of the received signal based on knife-edge diffraction together with reflections, transmission effects, and backscatter. This paper designs a short range underwater ultrasonic experimental system composed of an ultrasonic transceiver with wideband pulses and advanced spectral signal processing. We evaluate our proposed model with measurements made in a water tank with an obstacle moved between the transmitter and receiver. When the model includes all major propagation components and effects, it achieves an accuracy for localization of 97 % of the results in the range of twice the obstacle diameter in our test setup.