Oscillation of a Cable

by Austin Carlson

Submitted : Fall 2013

This project demonstrates a sinusoidal wave at a specific position and time. The projects purpose is to find the wave's (1) amplitude; (2) wavelength; (3) frequency; (4) wave speed; (5) the displacement; (6) the velocity; (7) the acceleration and (8) the net and total area underneath the wave. The equations were derived from algebraic manipulation of V=λf and the partial derivations of the equations of a transverse wave along with the integration of a transverse wave. Understanding the mathematical analysis behind sinusoidal waves is pivotal to understanding the behavior of waves, and the action of a vibrating string. The uses of the equations given are important to engineering because it allows you to find the values for the frequency and speed of the wave, which is essential for understanding the behavior of the wave. It is extremely important for an engineer to be able to understand not only why something happens, but the steps that create the outcome. This project illustrates a logical mathematical continuum that allows you to derive every needed unknown.

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