Prove that the spherical wave given by: ?(?,?) = (A ei k (r-vt))/r is indeed a solution of the three-dimensional wave equation Hint: Write the wave equation in spherical coordinates (therefore, you should use the Laplacian written in terms of r, ?, ?, and insert the solution given above into the wave equation.
Prove that the spherical wave given by: ?(?,?) = (A ei k (r-vt))/r is indeed a solution of the three-dimensional wave equation Hint: Write the wave equation in spherical coordinates (therefore, you should use the Laplacian written in terms of r, ?, ?, and insert the solution given above into the wave equation.
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Question
Prove that the spherical wave given by:
?(?,?) = (A ei k (r-vt))/r
is indeed a solution of the three-dimensional wave equation
Hint: Write the wave equation in spherical coordinates (therefore, you should use the Laplacian written in terms of r, ?, ?, and insert the solution given above into the wave equation.
Expert Solution
Step 1: 3d wave equation and laplacian operator in spherical coordinates.
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