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Resonance in a Closed Tube Constant Length, Changing Frequency.

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Presentation on theme: "Resonance in a Closed Tube Constant Length, Changing Frequency."— Presentation transcript:

1 Resonance in a Closed Tube Constant Length, Changing Frequency

2 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

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

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

5 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.

6 Overtones at Constant Length:

7 Closed Tube Resonant Frequencies:

8 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.

9 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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