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UNIVARIATE WAVEFORMS
Waves and Waveforms constitute a global phenomenon that makes its appearance in many areas of physics, but more interesting than the simple observation of the phenomenon as part of our everyday life is the mathematical analysis and the simulationtechniques used to analyse the phenomenon the scientific way. The description, using mathematical means, of their form and their movement opens a new window to a better understanding of those physical mechanisms that generate waves in the form that we find them in nature. Waves and Waveforms in nature can appear in many different forms. The most typical of all, and most easily observable, are the sea waves. Other forms of waves are the Acoustic Waves, the Vibrational Waves, the Electromagnetic Waves, as well as natural light itself. In the present we will try to present in a simple and understandable way all the basic mathematical principles governing the description and dissemination of waves in any form. The analysis will rely heavily on the two most basic types of waveforms, that of the "Sine" and that of the "Cosine". One of the first spectacular findings we will encounter, coming as a conclusion directly from the mathematical analysis of the waves, is that the "Superposition" principle holds true for all waveforms. In general terms what this principle is telling us is that any possible complex shape of ripples we can possibly observe in nature can be simply produced as the result of the addition between the appropriate combinations of "Sine" and "Cosine" waves with an appropriate "Amplitude" and "Frequency".
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Download "TheTransverseWave(.m)"
Download "TheTransverseWave(.fig)"
Download "TheLongitudinalWave(.m)"
Download "TheLongitudinalWave(.fig)"
Download "SnatchOfAWave"
Download "HyperTangent"
Download "SuperImposedWavesI"
Download "SuperImposedWavesII"
Download "SuperImposedWavesIII"
Download "SpectrumSuperImposedWaves"
Download "TwentySuperImposedWavesI"
Download "TwentySuperImposedWavesII"
Download "SumOfTwoTravellingWavesI"
Download "SumOfTwoTravellingWavesII"
Download "SumOfTwoTravellingWavesIII"
Download "TravellingWave"