Volume 2, Issue 4, October 2016, Page: 46-51

Generalized Equations for the Collinear Doppler Effect

Steven D. Deines, Donatech Technologies Inc., Fairfield, Iowa, USA

Received: Aug. 6, 2016;
Accepted: Sep. 23, 2016;
Published: Oct. 19, 2016

DOI: 10.11648/j.ijamtp.20160204.14 View 2771 Downloads 79

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.

Keywords

Doppler Effect, Sound Speed, Waves

To cite this article

Steven D. Deines,
Generalized Equations for the Collinear Doppler Effect,

*International Journal of Applied Mathematics and Theoretical Physics*. Vol. 2, No. 4, 2016, pp. 46-51. doi: 10.11648/j.ijamtp.20160204.14Copyright

Copyright © 2016 Authors retain the copyright of this article.

This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reference

[1]

Doppler, C. A. “Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels“, Proceedings of the Bohemian Society of Sciences, 1843.

[2]

Halliday, D., Resnick, R., Walker J., Fundamentals of Physics, 9th ed., Vol. 1, John Wiley and Sons, New York, 2011, p. 461-464.

[3]

Pickover, C. A., The Physics Book, Sterling, New York, 2011, p. 200.

[4]

Serway, R. A., and Faughn, J. S., College Physics, 6th ed., Vol. 1, Brooks/Cole Thomson Learning, 2003, p. 435-437.

[5]

Giambattista, A., Richardson, B. M., and Richardson, R. C., Physics, McGraw Hill, 2008, p. 433-437.

[6]

Gamon, G. and Cleveland, J. M., Physics: Foundations and Frontiers, Prentice-Hall International, Inc., 1960, p. 140-141.

[7]

Serway, R. A., and Jewett Jr., J. W., Physics for Scientists and Engineers, 6th ed., Vol. 1, Brooks/Cole Thomson, 2004, p. 522-527.

[8]

Knight, R. D., Physics for Scientists and Engineers, 2nd ed., Pearson Addison-Wesley, 2007, p. 623-626.

[9]

Sears, F. W. and Zemansky, M. W., University Physics, 3rd ed., Addison-Wesley Pub. Co., 1963, p. 521-523.

[10]

Morgan, J., Introduction to University Physics, Allyn and Bacon Inc., Vol 1, 1963, p. 475-478.

[11]

Jewett Jr., J. W. and Serway, R. A., Physics for Scientists and Engineers with Modern Physics, 8th ed., Vol. 1, Brooks/Cole Cengage Learning, 2010, p. 501.

[12]

Benumof, R. Concepts in Physics, Prentice Hall, Inc., 1965, p. 438-440.

[13]

Arens, A. B., Development of Concepts of Physics, Addison-Wesley, 1965, p. 476-477.

[14]

Semat, H., Fundamentals of Physics, 3rd ed., Hilt, Rinehart, and Winston, New York, 1960, p. 405-409.

[15]

Baez, A. V., The New College Physics, W. H. Freeman and Co., San Francisco, 1967, p. 228-229.

[16]

Fowler, R. G. and Meyer, D. I., Physics for Engineers and Scientists, Allyn and Bacon Company, 2nd Ed., 1962, p. 366-368.

[17]

Resnick, R. and Halliday, D., Physics, Part I, 1st ed., John wiley & Sons, New York, 1966, p. 512-515.

[18]

Giancoli, D. C. (2005) Physics, 6th ed., Pearson Prentice Hall, p. 338-341.

[19]

Ohanian, H. C., Physics, 2nd ed., W.W. Norton & Co., New York, 1989, p. 446-450.

[20]

Tipler, P. A., Physics for Scientists and Engineers, 4th ed., W. H. Freeman & Co., New York, 1999, p. 463-468.

[21]

Speyer, E., Six Roads from Newton: Great Discoveries in Physics, Wiley Popular Science, NY, 1994, p. 79.

[22]

Wolf, J., Barron’s AP Physics B, 4th ed., Barron’s Educational Series, Inc., 2008, p. 327.

[23]

De Pree, G., Physics, Broadway Books, NY, 2004, p. 78.

[24]

Weber, R. L., Manning, K. V., and White, M. W., College Physics, 4th ed., McGraw-Hill Book Company, 1965, p. 464-465.

[25]

Weidner, R. T., and Sells, R. L., Elementary Classical Physics, Vol. 2, Allyn and Bacon, Boston, 1965, p. 1049-1052.

[26]

Shortley, G. and Williams, D., Elements of Physics, Prentice-Hall Int., 4th ed., 1965, p. 463.

[27]

Cutnell, J. D. and Johnson, K. W., Physics, 9th ed., John Wiley and Sons, 2012, p. 484-490.

[28]

Young, H. D. and Freedman, R. A., University Physics, 12th ed., Pearson Addison-Wesley, San Francisco, 2007.

[29]

Halliday, D., Resnick, R., Krane, K.S., Fundamentals of Physics, 4th ed., John Wiley and Sons, New York, 1992, p. 457-460.

[30]

Rosen, J. and Gothard, L. Q., Encyclopedia of Physical Science, Infobase Publishing, (2009) p. 155, ISBN 0-8160-7011.

[31]

Serway, R. A. and Jewett Jr., J. W., Physics for Scientists and Engineers, Cengage Learning, 9th ed. (2014), p. 517-519.

[32]

Young, H. D., Adams, P. W., and Chastain, R. J., Sears and Zemansky’s College Physics, Pearson, 10th ed., (2016) p. 378-381.