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General Derivation of the Doppler Effect by Using a Space-Time Graph and Its Application
New Phys.: Sae Mulli 2017; 67: 1342~1347
Published online November 30, 2017;
© 2017 New Physics: Sae Mulli.

Gyhyuk KIM*

Gyeonggibuk Science High School, Uijeongbu 11601, Korea
Correspondence to:
Received July 3, 2017; Revised September 27, 2017; Accepted September 28, 2017.
cc This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
We derived the Doppler effect from geometric analysis of a space-time graph and found the general solution of the Doppler effect for 3-dimensional plane wave and spherical wave. In our general solution, we were able to treat symmetrically the motion of the wave source and that of detector and to integrate the formulas for the elastic wave and the light. Applying the formula to a relativistic aberration, we presented a simpler explanation of related physical concepts. In the case of 3-dimensional spherical waves, we expected a new transverse Doppler effect. The geometric derivation of the Doppler effect should allow students to study the Doppler effect more consistently and systematically.
PACS numbers: 01.40.-d, 03.30.+p
Keywords: Doppler effect, Space-time graph, 3-dimensional Doppler effect, Relativistic aberration, Transverse Doppler effect

March 2018, 68 (3)
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