Transverse Standing Waves in a Nonuniform Line and their Empirical Verifications ()
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.
Share and Cite:
H. 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.
Conflicts of Interest
The authors declare no conflicts of interest.
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.
|