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Published byJustine Poland Modified over 2 years ago

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Resonance in a Closed Tube Constant Length, Changing Frequency

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Review: Changing Length First resonance point: ≈ Half of difference ( ½ Δx). Decreases as f increases. Antinode to node. x initial ≈ ¼ λ … End correction! Distance between resonance points: Constant for same frequency. Decreases as f increases. Node to node. Δx = ½ λ

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Tube Length vs. Wavelength: L ≈ ¼ λ L ≈ 5 / 4 λ L ≈ ¾ λ

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Calculating Wavelength: L ≈ ¼ λ λ ≈ 4 L Δx = ½ λ λ = 2 Δx λ ≈ 4/3 L λ ≈ 4/5 L

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What about constant length? When resonating, net displacement of molecules is zero. Amplitude at resonance points is a relative maximum, because the sound is loudest. Constant length: –Constant velocity, b/c constant T. –Changing frequency & wavelength, b/c length changes.

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Overtones at Constant Length:

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Closed Tube Resonant Frequencies:

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Frequency, Wavelength, and Speed of ANY wave, including Sound: v = f λ Know two, find the third! Wavelength calculated as a fraction of L, or L calculated from λ. Speed calculated: v = 331.5 + 0.607 T. Frequency: measured or calculated.

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Open Tube Using the analysis of a closed tube as a guide, determine the frequencies at which an open tube of fixed length will resonate.

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