What Are the Origins of the Wave Equation?

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SUMMARY

The wave equation is defined as \(\frac{\partial^2 u}{\partial^2 t}=c^2\nabla^2 u\), which describes the propagation of waves in various media. Its origins are commonly found in introductory texts on partial differential equations (PDEs), such as "Partial Differential Equations" by David F. Griffiths. The equation illustrates the relationship between spatial and temporal changes in wave phenomena. Understanding this equation is essential for fields involving wave mechanics and physics.

PREREQUISITES
  • Partial Differential Equations (PDEs)
  • Wave Mechanics
  • Mathematical Analysis
  • Vector Calculus
NEXT STEPS
  • Study "Partial Differential Equations" by David F. Griffiths for foundational knowledge.
  • Explore the derivation of the wave equation in various physical contexts.
  • Learn about boundary conditions and their effects on wave propagation.
  • Investigate numerical methods for solving wave equations, such as finite difference methods.
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Students and professionals in physics, engineering, and applied mathematics who are interested in wave phenomena and their mathematical foundations.

coki2000
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Hi,
Why the wave equation is
\frac{\partial^2 u}{\partial^2 x}=c^2\nabla^2 u?
Where does it come from?Thanks.
 
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coki2000 said:
Hi,
Why the wave equation is
\frac{\partial^2 u}{\partial^2 x}=c^2\nabla^2 u?
Where does it come from?Thanks.

For me to consider your relationship the wave equation I would have to change it to:

\frac{\partial^2 u}{\partial^2 t}=c^2\nabla^2 u

The wave equation is probabley derived in every intro to PDE textbook.

https://www.amazon.com/dp/0486688895/?tag=pfamazon01-20
 
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