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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 8, Iss. 2 — Mar. 1, 1924
  • pp: 343–349

WAVE MOTION MODELS HAVING “DISPERSION” AND “FILTER” PROPERTIES

T. B. BROWN

JOSA, Vol. 8, Issue 2, pp. 343-349 (1924)
http://dx.doi.org/10.1364/JOSA.8.000343


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Citation
T. B. BROWN, "WAVE MOTION MODELS HAVING “DISPERSION” AND “FILTER” PROPERTIES," J. Opt. Soc. Am. 8, 343-349 (1924)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-8-2-343


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References

  1. G. A. Campbell, U. S. Patent No. 1227113, 1917. G. W. Pierce, Electrical Oscillations and Electric Waves, Ch. XVI. Several recent articles in the Bell System Technical Journal.
  2. H. Wigge. Ein Mechanisches Modell des Kettenleiters. Physik. ZS. 23, p. 653, 1921. Also ZS. f. Tech. Physik, 11, p. 302, 1921.
  3. For low frequencies ϕ is very small, so that cos ϕ may be represented by the approximate value (12/2). Equation (6) then gives ϕ=p√(m/k) and equation (7), V = px/ϕ = √(k/mx. If the elements are now sub-divided by N, then k″=Nk, m″=m/N, and x″=x/N; whence it is easily seen that the velocity remains unchanged.
  4. By the same reasoning used in the footnote, page 347, [equation] and [equation] which is Sellmeier's equation. Each additional pendulum adds an additional term of the form [equation] to the quantity under the radical.

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