Resonance in a Closed Tube

1
Resonance in a Closed Tube

• Constant Length,Changing Frequency

2
Review Changing Length

• First resonance point
• Half of difference ( ½ ?x).
• Decreases as f increases.
• Antinode to node.
• xinitial ¼ ? End correction!

• Distance between resonance points
• Constant for same frequency.
• Decreases as f increases.
• Node to node.
• ?x ½ ?

3
Tube Length vs. Wavelength
L ¼ ?
L ¾ ?
L 5/4 ?
4
Calculating Wavelength
?x ½ ?? 2 ?x
L ¼ ?? 4 L
? 4/3 L
? 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 Speedof ANY wave,
including Sound

• v f ?
• Know two, find the third!
• Wavelength calculated as a fraction of L, or L
  calculated from ?.
• Speed calculated v 331.5 0.607 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.