Partial differential equation-wave equation(2)
Can you help me to solve equation....
((∂²u)/(∂x²))(x,t)=(1/(c²))((∂²u)/(∂x²))(x,t)
Use the equation above to determine the dimension of the constant c
But why ((∂²u)/(∂x²))=LL⁻²and ((∂²u)/(∂x²))=LT⁻²........
How can it evolution?
Please help me to solve
The wave in equation in general isOriginally Posted by Steve Lam
Can you help me to solve equation....
((∂²u)/(∂x²))(x,t)=(1/(c²))((∂²u)/(∂x²))(x,t)
Use the equation above to determine the dimension of the constant c
But why ((∂²u)/(∂x²))=LL⁻²and ((∂²u)/(∂x²))=LT⁻²........
How can it evolution?
Please help me to solve
If the dimensions of t is T and x L, the due to the equality and the presence of u on both sides, the dimensions of c^2 is
, the dimension of c is like m/s and often c is called the wave speed.
As for the solution, if you introduce new coordinates
and
, then the PDE transforms to
which has as it's olution
or
 + g(x-c \,t)<br />
)
You have written an error in your PDE. Anyway the correct equation is:Can you help me to solve equation....
((∂²u)/(∂x²))(x,t)=(1/(c²))((∂²u)/(∂x²))(x,t)
Use the equation above to determine the dimension of the constant c
But why ((∂²u)/(∂x²))=LL⁻²and ((∂²u)/(∂x²))=LT⁻²........
How can it evolution?
Please help me to solve
The first term can be written as:
The dimensions of these are now:
In which I used V as the dimension of the dependent variable. This can be anything the PDE stands for, a pressure, a voltage, a current, ....
So using this on the complete PDE you get:
C is here the dimension of c. From which we can extract the dimension of c, i.e. C as:
coomast
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