The Doppler Frequency Shift Formula Derived by Directly Differentiating the Wave Speed Formula
DOI:
https://doi.org/10.14738/aivp.122.16567Keywords:
Doppler effect, Doppler frequency shift, Wave velocity equation, Calculus theoryAbstract
In the relative motion system composed of the wave source and observer, the wave velocity formula has been extended and modified, directly treating the velocity in the wave velocity formula as a variable. Then, the relationship between the change in velocity and the change in frequency can be obtained through differentiation. By further attributing the change in velocity to the relative motion between the wave source and observer, the Doppler shift formula can be derived. Compared with all existing methods for deriving Doppler formulas, the method proposed in this paper that performs differential analysis on the extended and modified wave velocity formula seems to be the simplest.
References
J.R. Potter, "Doppler Effect and Its Applications." Wiley-Interscience, 1969.
S.C. Tiwari, "Doppler effect and frequency-shift in optics," Institute of Natural Philosophy, Kusum Kutir, Mahamanapuri, Varanasi 221005, India, February 1, 2008.
R. J. Gleiser, "Doppler shift for a radar echo," Instituto de Matematica, Astronomia y Fisica, Universidad Nacional de Cordoba, Laprida 854,5000 Cordoba, Argentina, Nov. 1977 [Online]. Available: https://ieeexplore.ieee.org/document/1694110. [Accessed: May. 04, 2021].
Xu, M., "Principle and Application of Doppler Effect," Communication World, vol. 26, no. 02, pp. 313-315, 2019.
Li, Y., "Discussion on Doppler Effect Using Principle of Relative Motion," Journal of Correspondence Education (Natural Science Edition), vol. 2004, no. 06, pp. 18-20, 2004.
M. Rakhmanov, "Reflection of light from a moving mirror: derivation of the relativistic Doppler formula without Lorentz transformations," in IEEE Transactions on Education, vol. 56, no. 2, pp. 128-132, May 2013.
Y. Pierseaux, "Poincaré’s relativistic Doppler-Fizeau formula," IEEE, pp. 1-5, Aug. 2018.
J. Reignier, "An alternative derivation of Einstein's Doppler shift and aberration formulae," in IEEE Transactions on Education, vol. 60, no. 2, pp. 144-146, May 2017, doi: 10.1109/TE.2016.2594658.
Huang, X., "A New Method for Deriving Longitudinal Relativistic Doppler Effect," Spectroscopy Laboratory,
Wu, L. and Li, G., "A Derivation Scheme of Particle-like Electromagnetic Wave Doppler Effect," Journal of Yunnan Normal University (Natural Science Edition), vol. 36, no. 5, pp. 60-62, 2014. DOI: 10.3969/j.issn.1007-9793.2014.05.012.
Yang, J., "Derivation of Doppler Effect Formula Using Frequency Definition," Physics Bulletin, vol. 70, no. 12, pp. 10-11, 16, 2021. DOI: 10.3969/j.issn.0509-4038.2021.12.004. Yu, T. (2024). The Doppler Frequency Shift Formula Derived by Directly Differentiating the Wave Speed Formula. European Journal of Applied
Ding, Z., "Derivation and Application of Doppler Effect Formula for Electromagnetic Waves," Physics Teacher, vol. 43, no. 3, pp. 60, 69, 2022. DOI: 10.3969/j.issn.1002-042X.2022.03.020.
Chen, J., Zheng, C., Xiao, M., et al., "Derivation of Doppler Effect Formula Based on the Principle of Relativity," University Physics, vol. 42, no. 1, pp. 11-13, 2023. DOI: 10.16854/j.cnki.1000-0712.220199.
Li, Y., Yu, T., and Cai, W., "Derivation of Doppler Effect Formula for Sound Waves in Uniform and Variable Motion," Physics Bulletin, vol. 66, no. 12, pp. 82-84, 2016. DOI: 10.3969/j.issn.0509-4038.2016.12.026.
Huang, H. and Yang, J., "Derivation of Doppler Effect Formula Based on Kinematic Fundamentals," Physics Bulletin, vol. 71, no. 6, pp. 16-17, 2015. DOI: 10.3969/j.issn.0509-4038.2015.06.005.
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