This paper examines numerical methods for solving the continuation problem for one-dimensional acoustic equations, which is relevant in sound wave modeling tasks. The main focus is on applying the gradient method to inverse problems, allowing for the efficient reconstruction of acoustic field parameters from a limited set of data. An algorithm has been developed that includes computing the objective functional, its gradient, and performing minimization using iterative methods. The influence of noise level on the accuracy and stability of solutions has been analyzed. Numerical experiments have demonstrated that the proposed method achieves high accuracy in parameter reconstruction even under significant noise distortions. The analysis of computational costs confirmed the efficiency of the proposed approach. The obtained results have practical significance for applications in medical diagnostics (ultrasound tomography), geophysics (seismic exploration), technical diagnostics, and environmental monitoring.