Deriving the 3D Wave Equation: A Comprehensive Explanation

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SUMMARY

The discussion focuses on deriving the three-dimensional wave equation, specifically the equation of the form U_tt = U_xx + U_yy + U_zz. Participants clarify that this is a general wave equation, distinct from the Schrödinger wave equation. The need for a comprehensive understanding beyond basic definitions is emphasized, indicating that existing resources like Wikipedia may not provide sufficient depth.

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  • Understanding of partial differential equations
  • Familiarity with wave phenomena in physics
  • Knowledge of mathematical notation for derivatives
  • Basic concepts of three-dimensional space
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  • Study the derivation of the wave equation in three dimensions
  • Explore resources on partial differential equations
  • Investigate applications of the wave equation in physics
  • Learn about boundary conditions and their effects on wave behavior
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Students of physics, mathematicians, and educators seeking to deepen their understanding of wave equations and their applications in three-dimensional contexts.

Tuneman
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I would like to know how to derive the wave equation for a 3 dimensional case, I was looking it up on wikipedia, and their explanation wasn't very comprehensive, I was wondering if anyone knew of any other website that would be able to let me fullly understand it.

Edit: not the shrodinger wave equation, but general case of a wave.
 
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Not sure what you mean by 3 dimensional case but I think it is just a definition. If you see an equation of the form U_tt = U_xx + U_yy + U_zz we choose to call it the wave equation in three dimensions.
 

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