WJM  Vol.1 No.4 , August 2011
Transverse Standing Waves in a Nonuniform Line and their Empirical Verifications
Author(s) Haiduke Sarafian
ABSTRACT
We consider a one-dimensional elastic line with a linear varying density. Utilizing a Computer Algebra System (CAS), such as Mathematica symbolically we solve the equation describing progressive transverse waves yielding standing waves. For a set of suitable parameters the numeric mode of Mathematica displays and animates vibrating normal modes bringing the vibrations to life. We tailor a device that mimics the characteristics of the non-linearity; experimentally we explore its integrity.

Cite this paper
nullH. Sarafian, "Transverse Standing Waves in a Nonuniform Line and their Empirical Verifications," World Journal of Mechanics, Vol. 1 No. 4, 2011, pp. 197-202. doi: 10.4236/wjm.2011.14025.
References
[1]   Halliday, Resnick and J. Walker, “Fundamental of Physics,” 8th Edition, John Wiley & Sons, New York, 2008.

[2]   W. Bauer and D. W. Gary, “University Physics with Moder Physics,” McGraw Hill, New York, 2011.

[3]   C. K. George, “Vibrations and Waves,” John Wiley & Sons, New York, 2009.

[4]   P. F. Lewis, “Study of Eigenvalues of a Nonuniform String,” American Journal of Physics, Vol. 53, No. 8, 1985, p. 730. Hdoi:org/10.1119/1.14303H

[5]   S. Wolfram, “The Mathematica Book,” 4th Edition 2000, Cambridge University Press: MathematicaTM Software, Cambridge, V 8.01, 2011.

[6]   P. Wellin, R. Gayloard and S. Kamin, “An Introduction to Programming with Mathematica,” Cambridge University Press, Cambridge, 2005, pp. 1-30. Hdoi:org/10.1017/CBO9780511801303

[7]   a) Mechanical Oscillator, CP36803-01, Cenco Physics; b) Function Generator, BK Precision 4040; c) Oscillator Amplifier, Cenco 36891; d) Ammeter, Wavetek, 27XT.

[8]   Vertical Channel Valance, LowesTM hardware store, Bali.

[9]   Bernard and Epp, “Laboratory Experiments in College Physics,” 7th Edition, John Wiley & Sons, New York, 2008.

 
 
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