What is the correct mathematical relation connecting the fundamental frequencies of open and closed organ pipes ?
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Answer: A. fopen = 2 fclosed
Explanation
Open organ pipes support fundamental frequencies twice that of closed pipes. Boundary conditions dictate wavelength modes for standing waves inside tubes. An open pipe contains antinodes at both ends, doubling the fundamental frequency. Standing sound waves form inside musical instrument pipes due to acoustic reflections. Closed organ pipes have one node and one antinode at their boundaries. Acoustic resonance determines the pitch produced by wind instruments and pipes.
Musical instrument design relies on acoustic pipe resonance formulas for pitch. Organ builders adjust pipe lengths and open ends to produce specific musical notes. Understanding sound wave harmonics helps analyze vocal tract acoustics in speech. Option B incorrectly reverses the frequency ratio between open and closed pipes. Option C incorrectly claims open and closed pipes share identical fundamental frequencies. Option D uses an inverse relationship which contradicts standard acoustic wave physics.
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