Deriving the 3D Wave Equation: A Comprehensive Explanation

In summary, the conversation involved a request for information on deriving the wave equation for a 3 dimensional case. The person had searched on Wikipedia but found the explanation lacking and was looking for other resources to fully understand it. It was clarified that the equation in question was not the Schrodinger wave equation, but a general case of a wave. The concept of a 3 dimensional case was also discussed.
  • #1
Tuneman
41
0
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 explination 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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  • #2
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.
 

FAQ: Deriving the 3D Wave Equation: A Comprehensive Explanation

What is the 3D wave equation?

The 3D wave equation is a mathematical model used to describe the behavior of waves in three-dimensional space. It is a combination of the one-dimensional wave equation and the three-dimensional Laplace equation.

How is the 3D wave equation derived?

The 3D wave equation is derived by applying the principles of conservation of energy and momentum to a small volume element in a three-dimensional medium. This results in a differential equation that describes the propagation of waves in three dimensions.

What are the assumptions made when deriving the 3D wave equation?

The derivation of the 3D wave equation assumes that the medium is homogeneous, isotropic, and linear, meaning that its properties are the same in all directions and do not change with time or amplitude of the wave.

What are the applications of the 3D wave equation?

The 3D wave equation has many applications in various fields, including acoustics, electromagnetism, and fluid dynamics. It is used to study the behavior of sound waves, electromagnetic waves, and fluid waves, among others.

Are there any limitations to the 3D wave equation?

While the 3D wave equation is a powerful tool for describing the behavior of waves, it does have some limitations. It does not take into account factors such as damping, dispersion, and nonlinearity, which may be present in real-world situations. These limitations can be addressed by modifying the equation or using more complex models.

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