Abstract:
We show that dimensional analysis supplemented by physical insight determines if a wave has dispersion, without recourse to sophisticated mathematical tools. © 2007 American Association of Physics Teachers.
Registro:
Documento: |
Artículo
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Título: | Applying dimensional analysis to wave dispersion |
Autor: | Gratton, J.; Perazzo, C.A. |
Filiación: | INFIP CONICET, Dpto. de Física, Ciudad Universitaria, Pab. I, 428 Buenos Aires, Argentina Universidad Favaloro, Solís 453, 1078 Buenos Aires, Argentina Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET), Argentina
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Año: | 2007
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Volumen: | 75
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Número: | 2
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Página de inicio: | 158
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Página de fin: | 160
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DOI: |
http://dx.doi.org/10.1119/1.2372471 |
Título revista: | American Journal of Physics
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Título revista abreviado: | Am. J. Phys.
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ISSN: | 00029505
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029505_v75_n2_p158_Gratton |
Referencias:
- Bohren, C.F., Dimensional analysis, falling bodies, and the fine art of not solving differential equations (2004) Am. J. Phys, 72, pp. 534-537
- Pelesko, J.A., Cesky, M., Huertas, S., Lenz's law and dimensional analysis (2005) Am. J. Phys, 73, pp. 37-39
- The Pi theorem states that if p is the number of characteristic parameters (constant or variable) of the problem, and among them there are q that have independent dimensions, the number of dimensionless independent combinations that can be formed among them is equal to p-q. The original presentation of this theorem is due to E. Buckingham, On physically similar systems; Illustrations of the use of dimensional equations, Phys. Rev. 4, 345-376 (1914). It is also discussed in many books; see, for example, L. I. Sedov, Similarity and Dimensional Methods in Mechanics (Academic, New York, 1959); To be more precise, there can be a characteristic length as long as it does not play a role in the propagation of the waves, because in this case this length does not appear in the invariants ∏1, ∏n-2; Hall, H.E., (1974) Solid State Physics, , Wiley, New York
- Klemens, P.G., Dispersion relation for waves on liquid surfaces (1984) Am. J. Phys, 52, pp. 451-452
- Lighthill, J., (1978) Waves in Fluids, , Cambridge U. P, Cambridge
Citas:
---------- APA ----------
Gratton, J. & Perazzo, C.A.
(2007)
. Applying dimensional analysis to wave dispersion. American Journal of Physics, 75(2), 158-160.
http://dx.doi.org/10.1119/1.2372471---------- CHICAGO ----------
Gratton, J., Perazzo, C.A.
"Applying dimensional analysis to wave dispersion"
. American Journal of Physics 75, no. 2
(2007) : 158-160.
http://dx.doi.org/10.1119/1.2372471---------- MLA ----------
Gratton, J., Perazzo, C.A.
"Applying dimensional analysis to wave dispersion"
. American Journal of Physics, vol. 75, no. 2, 2007, pp. 158-160.
http://dx.doi.org/10.1119/1.2372471---------- VANCOUVER ----------
Gratton, J., Perazzo, C.A. Applying dimensional analysis to wave dispersion. Am. J. Phys. 2007;75(2):158-160.
http://dx.doi.org/10.1119/1.2372471