Understanding the Significance of the Linear Wave Equation in Wave Mechanics

AI Thread Summary
The discussion centers on the derivation of the linear wave equation for a string, specifically the equation ∂²y/∂x² = (1/v²) ∂²y/∂t². The original poster seeks to understand the significance of this equation and its applicability to various types of waves. A suggestion is made to share the derived equation for better clarity and understanding. A link to additional resources on wave equations is provided to aid in comprehension. Understanding this equation is crucial for grasping the fundamental principles of wave mechanics.
member 392791
Hello,

I am studying wave mechanics and I managed to derive the linear wave equation with a string. Now I don't understand the significance of the equation or why I can use a string oscillating to make it general and apply to all sorts of waves

Edit:

this one

\frac{\partial^2 y}{\partial x^2}=\frac{1}{v^2} \frac{\partial^2 y}{\partial t^2}
 
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What equation did you derive, can you post it.?
 
This may help you understanding, where this equation comes from:
http://amath.colorado.edu/courses/4380/2009fall/wave_equations.pdf
 
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