Generalized Equations for the Collinear Doppler Effect

Steven D. Deines

doi:doi:10.11648/j.ijamtp.20160204.14

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Generalized Equations for the Collinear Doppler Effect

Steven D. Deines

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 2, Issue 4)

Received: 6 August 2016 Accepted: 23 September 2016 Published: 19 October 2016

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Abstract

Some physics textbooks state that the equation for the collinear Doppler effect applies only to a reference frame fixed on the medium, while several textbooks ignore this limitation. The wavelength recorded by a moving observer can be transformed by the textbook Doppler equation in terms of only the source’s frequency and velocity, which demonstrates the textbook equation is inaccurate with a stationary source. The equation for the Doppler effect in textbooks approximates the observer’s frequency, even when the observer’s velocity is much less than the propagation velocity through the medium. The generalized Doppler equations for an observer are derived using infinite series for the moving observer in any inertial frame. The inaccuracy of the textbook equation is due to the false assumption that the observed wavelength in the observer’s frame is the same transmitted wavelength in the frame of the medium. It is also shown for sound that a moving source and moving observer with identical velocities through still air is the equivalent of having a stationary source and stationary observer with a wind of opposite velocity. This particular example also demonstrates that moving interferometers preserve wavelengths. These newly derived Doppler equations for the observer will add more precision with wave phenomena.

Published in	International Journal of Applied Mathematics and Theoretical Physics (Volume 2, Issue 4)
DOI	10.11648/j.ijamtp.20160204.14
Page(s)	46-51
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Doppler Effect, Sound Speed, Waves

References

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APA Style

Steven D. Deines. (2016). Generalized Equations for the Collinear Doppler Effect. International Journal of Applied Mathematics and Theoretical Physics, 2(4), 46-51. https://doi.org/10.11648/j.ijamtp.20160204.14

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ACS Style

Steven D. Deines. Generalized Equations for the Collinear Doppler Effect. Int. J. Appl. Math. Theor. Phys. 2016, 2(4), 46-51. doi: 10.11648/j.ijamtp.20160204.14

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AMA Style

Steven D. Deines. Generalized Equations for the Collinear Doppler Effect. Int J Appl Math Theor Phys. 2016;2(4):46-51. doi: 10.11648/j.ijamtp.20160204.14

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@article{10.11648/j.ijamtp.20160204.14,
  author = {Steven D. Deines},
  title = {Generalized Equations for the Collinear Doppler Effect},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {2},
  number = {4},
  pages = {46-51},
  doi = {10.11648/j.ijamtp.20160204.14},
  url = {https://doi.org/10.11648/j.ijamtp.20160204.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20160204.14},
  abstract = {Some physics textbooks state that the equation for the collinear Doppler effect applies only to a reference frame fixed on the medium, while several textbooks ignore this limitation. The wavelength recorded by a moving observer can be transformed by the textbook Doppler equation in terms of only the source’s frequency and velocity, which demonstrates the textbook equation is inaccurate with a stationary source. The equation for the Doppler effect in textbooks approximates the observer’s frequency, even when the observer’s velocity is much less than the propagation velocity through the medium. The generalized Doppler equations for an observer are derived using infinite series for the moving observer in any inertial frame. The inaccuracy of the textbook equation is due to the false assumption that the observed wavelength in the observer’s frame is the same transmitted wavelength in the frame of the medium. It is also shown for sound that a moving source and moving observer with identical velocities through still air is the equivalent of having a stationary source and stationary observer with a wind of opposite velocity. This particular example also demonstrates that moving interferometers preserve wavelengths. These newly derived Doppler equations for the observer will add more precision with wave phenomena.},
 year = {2016}
}

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TY  - JOUR
T1  - Generalized Equations for the Collinear Doppler Effect
AU  - Steven D. Deines
Y1  - 2016/10/19
PY  - 2016
N1  - https://doi.org/10.11648/j.ijamtp.20160204.14
DO  - 10.11648/j.ijamtp.20160204.14
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 46
EP  - 51
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20160204.14
AB  - Some physics textbooks state that the equation for the collinear Doppler effect applies only to a reference frame fixed on the medium, while several textbooks ignore this limitation. The wavelength recorded by a moving observer can be transformed by the textbook Doppler equation in terms of only the source’s frequency and velocity, which demonstrates the textbook equation is inaccurate with a stationary source. The equation for the Doppler effect in textbooks approximates the observer’s frequency, even when the observer’s velocity is much less than the propagation velocity through the medium. The generalized Doppler equations for an observer are derived using infinite series for the moving observer in any inertial frame. The inaccuracy of the textbook equation is due to the false assumption that the observed wavelength in the observer’s frame is the same transmitted wavelength in the frame of the medium. It is also shown for sound that a moving source and moving observer with identical velocities through still air is the equivalent of having a stationary source and stationary observer with a wind of opposite velocity. This particular example also demonstrates that moving interferometers preserve wavelengths. These newly derived Doppler equations for the observer will add more precision with wave phenomena.
VL  - 2
IS  - 4
ER  -

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Author Information

Steven D. Deines

Donatech Technologies Inc., Fairfield, Iowa, USA

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APA Style

Steven D. Deines. (2016). Generalized Equations for the Collinear Doppler Effect. International Journal of Applied Mathematics and Theoretical Physics, 2(4), 46-51. https://doi.org/10.11648/j.ijamtp.20160204.14

Copy | Download

ACS Style

Steven D. Deines. Generalized Equations for the Collinear Doppler Effect. Int. J. Appl. Math. Theor. Phys. 2016, 2(4), 46-51. doi: 10.11648/j.ijamtp.20160204.14

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AMA Style

Steven D. Deines. Generalized Equations for the Collinear Doppler Effect. Int J Appl Math Theor Phys. 2016;2(4):46-51. doi: 10.11648/j.ijamtp.20160204.14

Copy | Download

@article{10.11648/j.ijamtp.20160204.14,
  author = {Steven D. Deines},
  title = {Generalized Equations for the Collinear Doppler Effect},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {2},
  number = {4},
  pages = {46-51},
  doi = {10.11648/j.ijamtp.20160204.14},
  url = {https://doi.org/10.11648/j.ijamtp.20160204.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20160204.14},
  abstract = {Some physics textbooks state that the equation for the collinear Doppler effect applies only to a reference frame fixed on the medium, while several textbooks ignore this limitation. The wavelength recorded by a moving observer can be transformed by the textbook Doppler equation in terms of only the source’s frequency and velocity, which demonstrates the textbook equation is inaccurate with a stationary source. The equation for the Doppler effect in textbooks approximates the observer’s frequency, even when the observer’s velocity is much less than the propagation velocity through the medium. The generalized Doppler equations for an observer are derived using infinite series for the moving observer in any inertial frame. The inaccuracy of the textbook equation is due to the false assumption that the observed wavelength in the observer’s frame is the same transmitted wavelength in the frame of the medium. It is also shown for sound that a moving source and moving observer with identical velocities through still air is the equivalent of having a stationary source and stationary observer with a wind of opposite velocity. This particular example also demonstrates that moving interferometers preserve wavelengths. These newly derived Doppler equations for the observer will add more precision with wave phenomena.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Generalized Equations for the Collinear Doppler Effect
AU  - Steven D. Deines
Y1  - 2016/10/19
PY  - 2016
N1  - https://doi.org/10.11648/j.ijamtp.20160204.14
DO  - 10.11648/j.ijamtp.20160204.14
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 46
EP  - 51
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20160204.14
AB  - Some physics textbooks state that the equation for the collinear Doppler effect applies only to a reference frame fixed on the medium, while several textbooks ignore this limitation. The wavelength recorded by a moving observer can be transformed by the textbook Doppler equation in terms of only the source’s frequency and velocity, which demonstrates the textbook equation is inaccurate with a stationary source. The equation for the Doppler effect in textbooks approximates the observer’s frequency, even when the observer’s velocity is much less than the propagation velocity through the medium. The generalized Doppler equations for an observer are derived using infinite series for the moving observer in any inertial frame. The inaccuracy of the textbook equation is due to the false assumption that the observed wavelength in the observer’s frame is the same transmitted wavelength in the frame of the medium. It is also shown for sound that a moving source and moving observer with identical velocities through still air is the equivalent of having a stationary source and stationary observer with a wind of opposite velocity. This particular example also demonstrates that moving interferometers preserve wavelengths. These newly derived Doppler equations for the observer will add more precision with wave phenomena.
VL  - 2
IS  - 4
ER  -

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