Resonance in Air Columns

Sound waves from one source can cause an identical source to vibrate in resonance. Suppose that two tuning forks of identical frequency, mounted on wooden boxes of identical length and open at one end, are placed 1 metre apart. When the first tuning fork is struck and then silenced, a sound of the same frequency comes from the second tuning fork even though it was not struck. Resonance has occurred because the forks have the same natural frequency. Energy has been transferred from one fork to the other by sound waves.

Resonance Air Columns

If an air column is closed at one end and open at the other, it is referred to as a closed air column. An example of this type of air column is in the above image.

When a vibrating tuning fork is held over the open end of such a column and the length of the column is increased, it is found that the loudness increases sharply at very specific lengths. If a different tuning fork is used, the same result occurs except the maxima occur at different lengths.

When longitudinal sound waves are emitted by a tuning fork, some of them travel down the closed air column. The end of the tube reflects the sound waves back. A node is formed at the bottom of the column, and, since the air is free to move at the top of the tube, a loop forms there.

When the resonance first occurs, the column is 1/4 l in length, since a single loop and node are formed. The next possible lengths with a node at one end and a loop at the other are 3/4 l, 5/4 l , and so on. Thus, the resonant lengths in a closed air column occur at 1/4 l , 3/4 l , 5/4 l, and so on.


Closed Air Columns

First Resonant
Frequency 		Second Resonant Frequency Third Resonant
Frequency

Different resonant frequencies with a fixed length.

First Resonant
Frequency 		Second Resonant Frequency Third Resonant
Frequency



Open Air Columns

Resonant lengths of an open air column with a sound of a given frequency.

Open and closed air columns that resonate have been used in most cultures as musical instruments. Today instruments in Western culture are divided into the classes: windwoods and brass. The trumpet

is an air column open at both ends

A quick summary is shown in this chart

Notes to be Made

  1. Define what resonance is.
    What must exist between the the vibrating source and the object to be resonated ?
  2. What does the tem "natural frequency" mean?
  3. There are two types of air columns. They are a) ________ and b) ______
    Give an example of each (think in terms of musical instruments).
  4. An open at both end air column resonates in __________ multiples of wavelengths.
    A closed at one end air column can resonate in _______ multiples of wavelengths.
  5. Closed at one end air columns have a ____________ at the closed end and a _____________ at the open end.
  6. Open air columns have two ________, one at each end or openning.
  7. The length of any air column (open or closed) must be "in tune" with the resonating energy source. What would be observed when this condition is met?
  8. In the three sets of pictures how could you determine the wavelength of each of the waves shown?
  9. An air column closed at on end has a distance between two loud sounds of 26.0 cm. What is the wavelength of the sound producing the resonance?
  10. A bugle is essentially an air column open at both ends. If the length of a particular bugle is 2.65 m, if the speed of sound is 344 m/s.
    1. Determine the lowest frequency note that can be played on this bugle.
      Ans: 64.9 Hz
    2. Determine the next two higher frequencies that will produce resonance.
      Ans: 130 Hz, & 195 Hz
  11. A trombone is playing an G (98.0 Hz) as its first harmonic. A trombone is an open at both ends air column.
    1. Determine the second harmonic.
    2. What would the frequency be of the G note one octave above, and what is the frequency of the C note between these two G notes?
    3. If the temperature of the air is 20.0oC, what is the length of tubing being used?
      Ans: 1.75 m