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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. xinitial ≈ 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:**

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**Calculating Wavelength:**

Δx = ½ λ λ = 2 Δx L ≈ ¼ λ λ ≈ 4 L 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 = 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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