Abstract
The classical Doppler was discovered by the Austrian physicist, Christian Doppler (1803–1853), who in 1842 published an article describing the frequency shift for a wave emitted by a source in motion. Three years later, an experiment confirmed this theory: 15 trumpeters were placed on board a train and some music-lovers experimenters on a train station platform. When the train arrived, the trumpeters continued to play and the emitted sound had a lower pitch after train had passed, as predicted by Doppler. This effect is frequently observed in acoustics, as shown by train and the trumpeters, as well as in electromagnetism, by the “red-shift” measured by astrophysicists, and it is utilized in speed radars. This effect may be used to enable a stationary observer to deduce significant data about a moving target such as its speed and whether it is approaching or receding (Photo 7.1).
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Notes
- 1.
Willis Eugene Lamb Jr (1913–2008) was an American physicist. He obtained his PhD on neutron scattering in 1938 at Berkeley under the supervision of Robert Oppenheimer, and published an original work in his own name on the effective temperature: Capture of neutrons by atoms in a crystal, Phys. Rev. 55, 190–197 (1939). He later taught at several faculties. He was awarded the Nobel Prize in 1955 for studies he performed in 1947 on the fine structure of the hydrogen atom concerning the doubling of hydrogen rays induced by virtual fluctuations of the electromagnetic field (second quantization). This effect is known as the Lamb shift.
- 2.
Peter Debye (1884–1966) was a Dutch chemist and physicist. He read electro-technics at Aachen under the supervision of Arnold Sommerfeld. In 1912, he derived the equations of the dipole moment in terms of temperature and developed a specific heat theory for very low temperatures by introducing the notion of phonons. In 1936, he was awarded the Nobel Prize in chemistry for “contributing to the study of the molecular structure through research on the dipolar moment and X-ray diffraction in gases.” In 1938, he refused the insistent treaties of the Nazis to take German nationality and fled to the United States, where he worked at Cornell University and became head of the chemistry department. The Debye is the unit of the dipole moment of molecules
Peter Debye (Public domain).
- 3.
Woldemar Voigt (1850–1919) was a German physicist (Photo 6.2). At the University of Gottingen, his interests centered on crystallography and thermodynamics. In 1887, he published ‘Über das Doppler’sche princip’ (On the Principles of the Doppler Effect) in Göttinger Nachrichten (7), pp. 41–61 (1887), which was in fact one of the first theories involving non-varying speed of light, and thus prefigured the theory of relativity. In the same paper, he postulated the invariance of laws of physics in the translation frames. He suggested that the Michelson-Morley experiment in 1881 (showing that the Earth’s motion had no effect on the speed of light) was due to Doppler effect within the absolute space-time frame, without nevertheless, although he did not challenge the principle of the ether—a medium with “magical” properties (harder than diamond, thinner than air!) that was postulated to explain the propagation of electromagnetic waves. Furthermore, he proposed a transformation of coordinates of a frame of reference that was also developed completely by Lorentz independently of Voigt. The name of Lorentz is still associated with this transformation. The work of Andreas Ernst and Jong-Ping Hsu on the history of sciences, First Proposal of the Universal Speed of Light by Voigt in 1887, Chinese Journal of Physics, vol. 39(3) pp. 211–230 (2001), shows the importance and Voigt’s innovative work in its context, without diminishing the contributions of Lorentz or Einstein. For the record, it was Voigt who invented the word “tensor” in the mathematical sense in 1899.
- 4.
Beynon and Grant: Evaluation of the Doppler-Broadened Single-Level and Interference Functions, Nuclear Science and Engineering, 17, p. 545 (1963).
- 5.
Dominique Grenèche : Physique des réacteurs à haute température, évaluation des sections efficaces résonnantes du Thorium 232, interprétation d’expériences critiques américaines [Physics of high-temperature reactors, evaluation of resonant cross sections of Thorium 232, interpretation of critical US experiments.], PhD thesis, University of Orsay (1973).
- 6.
Historically, the quantity ζ was noted i, but the confusion with the complex number struck us as most unfortunate.
- 7.
R. S. Keshavamurthy, R. Harish: Use of Padé approximations of the analytical evaluation of the J(ξ, β) function and its temperature derivative, Nuclear Science and Engineering, Vol. 115, pp. 81–88 (1993).
- 8.
Arthur Ginsberg , Martin Becker : An improved series representation of Doppler-broadened resonance absorption, Nuclear Science and Engineering, Vol. 56, No. 1 pp. 106–107 (1975). The reader should pay careful attention to a small typing mistake in \( {A}_m\equiv {\left(-1\right)}^m/\sqrt{1+m} \) and change the coefficient sign, since the equation should not be \( {A}_m\equiv {\left(-1\right)}^2/\sqrt{1+m} \).
- 9.
R. Bonalumi: Some Remarks about the Surface Resonance Absorption in Heterogeneous Reactors, Energia Nucleare, Vol. 12, No. 4, pp.189–204 (April 1965). In this work, Bonalumi develops the calculation of the effective area by taking into account the lattice effects. His approach uses the Dancoff effect and he proposes the use of correction coefficients for different moderators (water, heavy water, air).
- 10.
Jean Mougey , Roberto Solanolla : Intégrale de résonance effective de l’uranium 238 [Effective resonance integral of Uranium-238], Note CEA-N 503 (1965).
- 11.
Porter and Thomas, Physical Review No 104, 483 (1956).
- 12.
T.P. Ribeiro de Campos , A.S. Martinez : Approximate calculation of the resonance integral for isolated resonances, Nuclear Engineering and Design, 102, 211–238 (1989).
- 13.
A. Sanchez , A. Dos Santos : The intermediate resonance parameters for the multi-group formalism, Nuclear Engineering and Design, 387–400 (1999).
- 14.
N.M. Steen , Nuclear Science and Engineering, 38, 244 (1969).
- 15.
D. Neberejnev , C. Mounier , R. Sanchez : The influence of crystalline binding on resonance absorption and reaction rates, Nuclear Science and Engineering 131, pp. 222–229 (1999).
- 16.
H. Serizawa , K. Fukuda , T. Shiratori. T. Fujino, N. Sato and K. Yamada: Unusual variation of temperature factor of uranium dioxide at high temperature, Journal of Alloys and Compounds, Vol. 271–273, 1998, pp. 386–390.
- 17.
This is the value in the American code MICBURN-E or deduced from the measurements made in the MINERVE reactor by H. Tellier .
- 18.
A. Meister , A. Santamarina : The effective temperature for Doppler broadening of neutron resonances in UO2, International Conference on the Physics of Nuclear Science and Technology, Long Island, USA, October 1998, pp. 233–239.
- 19.
G.M. Roe: The Absorption of Neutrons by Doppler Broadened Resonances, General Electric Company, Knolls Atomic Power Laboratory, KAPL-1241, New York, 1954.
- 20.
A. Keane: Resonance absorption in a slab with a parabolic temperature distribution, Atomic Energy Research Establishment, AERE R/M 198, Harwell, UK, 1958.
- 21.
A. Reichel, A. Keane: Resonance absorption in a cylindrical fuel rod with radial temperature variation, Proceedings of the Royal Society, NSW 94, pp. 215–225, 1961.
- 22.
G. Rowlands : Resonance absorption and non-uniform temperature distributions, Journal of Nuclear energy, parts A/B, 16, 235–236 (1962). After completing his PhD in theoretical physics on magnetism at the University of Leeds, George Rowlands (1932- ) joined Harwell in 1957, where he worked on fission first then on fusion. In 1966, he joined the University of Warwick where he taught non-linear physics problems and plasma physics until his retirement in 2000. He wrote a book on the latter subject: Nonlinear Waves, Solitons and Chaos, Cambridge University Press, 1990.
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Marguet, S. (2017). Doppler Effect. In: The Physics of Nuclear Reactors. Springer, Cham. https://doi.org/10.1007/978-3-319-59560-3_6
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