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I am looking for an equation that describes the energy distribution within the space containing a vibrating string. Think of it as being an enclosed evacuated box with a rubber band or piano wire connected to each end, and is vibrating at the primary frequency. I can guess that the length, deflection distance, width, elasticity, and density of the band would all come into play, and no doubt several other parameters which I have not yet thought of.

I am sure there are basic wave mechanical equations for vibrating strings vs frequency and length in all the standard text books, but can anyone offer me advise on how to get an energy distribution at point L between two fixed points from this vibrating string scenario?

Thank you in advance for your consideration.

Steve.