Dispersive Wave: Difference between revisions

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Since the [https://belize.math.uwaterloo.ca/mediawiki/index.php/Glossary#Phase_Velocity|phase_velocity] is <math>\frac{\omega}{k}</math>, if <math>\omega(k) = c k</math> for some scalar <math>c</math>, then the phase velocity is <math>c</math>, independent of <math>k</math>, so that all waves, no matter their wavelength, travel at the same speed.  But if the dispersion relation is some other function of <math>k</math>, waves of different wavelengths travel at different speeds, leading to dispersion.
Since the <a href="https://belize.math.uwaterloo.ca/mediawiki/index.php/Glossary#Phase_Velocity">phase velocity</a> is <math>\frac{\omega}{k}</math>, if <math>\omega(k) = c k</math> for some scalar <math>c</math>, then the phase velocity is <math>c</math>, independent of <math>k</math>, so that all waves, no matter their wavelength, travel at the same speed.  But if the dispersion relation is some other function of <math>k</math>, waves of different wavelengths travel at different speeds, leading to dispersion.

Revision as of 09:53, 19 May 2015

Since the <a href="https://belize.math.uwaterloo.ca/mediawiki/index.php/Glossary#Phase_Velocity">phase velocity</a> is , if for some scalar , then the phase velocity is , independent of , so that all waves, no matter their wavelength, travel at the same speed. But if the dispersion relation is some other function of , waves of different wavelengths travel at different speeds, leading to dispersion.

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