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.
xinitial ≈ 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:

4. Calculating Wavelength:
Δx = ½ λ λ = 2 Δx
L ≈ ¼ λ λ ≈ 4 L
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.