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There's an error in that the type of pipe for each of the two fundamental frequencies as described in your comment don't match the problem description. The pipe with a fundamental frequency of 440Hz is open-closed, and the pipe with a fundamental frequency of 660Hz is open-open. You actually said "closed-closed", which isn't even an option, but even if ...


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Musical instruments are forced resonant objects, so we must break this problem into steady state and transient solutions. Any analysis that ignores either solution is incomplete. Strings are the simplest, so lets start there. A string vibrates at $ \omega = n k /L$ where $n$ is an integer, $L$ is the length of the string and $k$ is a constant incorporating ...



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