Deriving Wave Equation by Vector Approach

In summary, The conversation is about evaluating someone's work on the wave equation and vibrating system using a vector approach. The person is open to corrections and acknowledges the help and support. They discuss computing the Laplacian of a vector and clarify that position vector can also be considered a scalar field. The conversation ends with gratitude.
  • #1
danong
47
0
Hi there,
i would like everyone to evaluate my working here,
this is my attempt to wave equation / vibrating system using vector approach.
please correct me if i had made some mistakes.


Your help is much appreciated,
Thanks, and have a nice day. :smile:


Regards,
Daniel.
 

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  • #2
I didn't know that we can compute the Laplacian of a vector.
[tex]\nabla^2 \vec{U}[/tex] :confused:
 
  • #3
matematikawan said:
I didn't know that we can compute the Laplacian of a vector.
[tex]\nabla^2 \vec{U}[/tex] :confused:

erm sorry i don't quite understand your question,
why is it not?

and thanks for looking at my work =)
 
  • #4
i think i got what you mean,
position vector is considered as scalar field as well, isn't it?
it is just a notation of denoting the field.
 

1. What is the wave equation and why is it important?

The wave equation is a mathematical representation of how waves behave and propagate through a medium. It is important because it allows scientists to predict and understand the behavior of various types of waves, such as sound waves and electromagnetic waves.

2. What is the vector approach to deriving the wave equation?

The vector approach to deriving the wave equation involves using vector calculus to describe the behavior of waves. This method takes into account the direction and magnitude of the wave as well as the properties of the medium it is traveling through.

3. How is the wave equation derived using the vector approach?

The wave equation can be derived by applying the principles of vector calculus, such as the divergence and curl operators, to the fundamental equations of motion for a wave. This results in a set of partial differential equations that describe the behavior of the wave.

4. What are the advantages of using the vector approach to derive the wave equation?

The vector approach allows for a more comprehensive and accurate representation of waves, as it takes into account the direction and magnitude of the wave. It also allows for more complex and realistic scenarios to be modeled, such as waves traveling through non-uniform media.

5. Are there any limitations to the vector approach in deriving the wave equation?

One limitation of the vector approach is that it can be more mathematically complex and requires a strong understanding of vector calculus. Additionally, it may not be suitable for all types of waves, as some may require a different approach for accurate representation.

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