An open organ pipe filled with air has a fundamental frequency 500 Hz. The first harmonic of another organ pipe closed at one end and filled with carbon dioxide has the same frequency as that of the first harmonic of the open organ pipe. Calculate the length of each pipe. Assume that the velocity of sound in air and in carbondioxide to be 330 and 264 m s⁻¹ respectively. Choose the option containing the correct final result.
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Question

An open organ pipe filled with air has a fundamental frequency 500 Hz. The first harmonic of another organ pipe closed at one end and filled with carbon dioxide has the same frequency as that of the first harmonic of the open organ pipe. Calculate the length of each pipe. Assume that the velocity of sound in air and in carbondioxide to be 330 and 264 m s⁻¹ respectively. Choose the option containing the correct final result.

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G1 Physics · Accepted Answer

Step 1: Use v = √(B/ρ) in a fluid, v = √(Y/ρ) for longitudinal waves in a solid, or v = √(γRT/M) for an ideal gas. Step 2: Form any required ratio before substituting values. Step 3: Evaluate with the data given. Final: D: 33 cm and 13.2 cm.