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Show that the fundamental frequency of vibration of the air column in a pipe open at both ends is double that of a pipe of the same length and closed at one end. |
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Answer» Let LO and LC be the lengths of a pipe open at both ends and a pipe closed at one end, respectively. Let nO and nC be their corresponding fundamental frequencies. Then, ignoring the end corrections, nO = \(\frac v{2L_O}\) and nC = \(\frac v{4L_C}\) where v is the speed of the sound in air. Given that LO = LC = L (say), nO = \(\frac v{2L}\) and nO = \(\frac v{4L}\) ∴ nO = 2 \((\frac v{4L})\) = 2nC |
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