BibTex Citation Data :
@article{JPA26584, author = {Radha Firaina and Yudhiakto Pramudya}, title = {Numerical Analysis of the Doppler Effect in Circular Motion with Modulated Angular Velocity Using Python}, journal = {Journal of Physics and Its Applications}, volume = {7}, number = {4}, year = {2025}, keywords = {Doppler Effect; Circular Motion; Modulated Angular Velocity; Numerical Analysis; Python Simulation}, abstract = { 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. }, issn = {2622-5956}, pages = {143--149} doi = {10.14710/jpa.v7i4.26584}, url = {https://ejournal2.undip.ac.id/index.php/jpa/article/view/26584} }
Refworks Citation Data :
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.
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