TITLE:
Transverse Standing Waves in a Nonuniform Line and their Empirical Verifications
AUTHORS:
Haiduke Sarafian
KEYWORDS:
Nonuniform Line, Standing Waves, Airy Functions, Mathematica
JOURNAL NAME:
World Journal of Mechanics,
Vol.1 No.4,
September
7,
2011
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.