The primary function of passive sonar is to detect a target amidst the ambient noise that is present in the background and the Transmission Loss associated with underwater sound propagation. Sonar performance modeling [1] is used to quantify the sonar performance in the context of effective detection by having a careful and detailed analysis of the terms involved in the passive sonar equation [2]-[4]. The depiction of Transmission Loss curve, low frequency ambient noise mapping, solution of Receiver Operating Characteristics (ROC) curve with the help of complex mathematical models is essential for the effective usage of sonar and help us visualize and solve the real world problems. With the help of the Receiver Operating Characteristics (ROC) for varying values of (Signal to Noise Ratio) SNR, Detection Threshold (DT) and the study of existing models and techniques to find the Transmission Loss, effective range can be calculated. The