Numerical Analysis of the Doppler Effect in Circular Motion with Modulated Angular Velocity Using Python - Firaina, Radha; Pramudya, Yudhiakto (Journal of Physics and Its Applications, 2025)
This study presents a numerical simulation of the Doppler effect for an object in circular motion with time-modulated angular velocity, developed using the Python programming language. The model computes angular velocity, angular position, and observed frequency as functions of time based on a modified Doppler formulation. Two simulation models were implemented: an interactive mode using an IPython widget slider to vary the modulation constant (0 ≤ b ≤ 1), and a comparative mode evaluating three representative modulation strengths (b = 0.15, 0.20, 0.25). The results demonstrate that the modulation of angular velocity produces periodic fluctuations in the observed frequency, consistent with theoretical predictions. Sensitivity testing confirmed numerical stability (∆f < 0.01 Hz) with smaller time steps (∆t = 0.01 s), validating the robustness of the computational model. These findings quantitatively reveal the relationship between modulation parameters and Doppler frequency shifts, providing a reproducible and pedagogically effective framework for studying non-uniform circular motion and its physical implications in astrophysical and acoustic systems.