Open-end Air Columns

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Open-end Air Columns

• An open air column has a fundamental frequency of
  200 Hz. What is the frequency of the second
  harmonic (first overtone)?
• A. 300 Hz B. 400 Hz C. 600 Hz D. 800 Hz
• If the length of the air column is increased, the
  frequency of the fundamental is
• A. increased B. decreased C. the same

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Open-end Air Columns

• An open air column has a fundamental frequency of
  200 Hz. What is the frequency of the second
  harmonic (first overtone)?
• A. 300 Hz B. 400 Hz C. 600 Hz D. 800 Hz
• If the length of the air column is increased, the
  frequency of the fundamental is
• A. increased B. decreased C. the same

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Resonance in Closed Air Columns

• 3U Physics

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Resonance in Closed-End Air Columns

• If one end of an air column is closed off, it
  must have a node at that end.
• The first harmonic of a closed-end air column is
  therefore

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Resonance in Closed-End Air Columns

• If one end of an air column is closed off, it
  must have a node at that end.
• The first harmonic of a closed-end air column is
  therefore

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Resonance in Closed-End Air Columns

• If one end of an air column is closed off, it
  must have a node at that end.
• The first harmonic of a closed-end air column is
  therefore
• Note that l 4L (or L l/4).

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Higher Harmonics

• The next higher harmonic that can be produced is

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Higher Harmonics

• The next higher harmonic that can be produced is

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Higher Harmonics

• The next higher harmonic that can be produced is
• l 4L/3 or L 3l/4

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Higher Harmonics

• The next higher harmonic that can be produced is
• l 4L/3 or L 3l/4
• This harmonic is called the 3rd (and not the 2nd)
  harmonic because its frequency is 3 times that of
  the fundamental frequency.

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Higher Harmonics

• Similarly, the next higher harmonic is the fifth
  harmonic
• l 4L/5 or L 5l/4

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Longitudinal Waves

• What do these standing waves actually look like?

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Longitudinal Waves

• What do these standing waves actually look like?

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Closed-End Air Columns Example

• A closed-end air tube resonates to a tuning fork
  of 480 Hz at lengths of 53.0 cm and 88.5 cm.
  What is the speed of sound in air?

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Closed-End Air Column Example

• A closed-end air tube resonates to a tuning fork
  of 480 Hz at lengths of 53.0 cm and 88.5 cm.
  What is the speed of sound in air?

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Closed-End Air Column Example

• A closed-end air tube resonates to a tuning fork
  of 480 Hz at lengths of 53.0 cm and 88.5 cm.
  What is the speed of sound in air?
• The difference between one harmonic and the next
  is a half-wavelength (for open or closed-ends).

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Closed-End Air Columns Example

• A closed-end air tube resonates to a tuning fork
  of 480 Hz at lengths of 53.0 cm and 88.5 cm.
  What is the speed of sound in air?

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More Practice

• Lab Closed Air Columns and the Speed of Sound