THE EXPERIMENT

Two small loudspeakers are provided on stands that allow them to be adjusted in height and orientation; lateral position is changed simply by moving the stands about inside the box. Small transformers outside the box match the speakers to:

  1. An audio oscillator that has both sine wave and square wave outputs, and an accurate digital display of frequency. The sine wave output is used to drive the speaker.
  2. An oscilloscope that serves as a visual indicator of power into the receiver speaker.

To place the equipment into operation, first position the two speakers in some position of your choice within the box. (It is strongly recommended that your first choice of position and orientation be particularly simple.)

The scope should be set for a sensitivity of 20 mV/div., and the horizontal time sweep switched to 1 ms/div. The audio generator output level should be set to mid-range.

Now, sweep the frequency control on the oscillator through the range of about 300 Hz to 1000 Hz, and notice sharp maxima in the height of the pattern on the scope screen. Each of these is a resonance of the enclosure. Notice that between resonances of the box, the driver speaker transmits relatively little energy directly to the receiver, even if they are fairly close.

Record the frequency (as accurately as you can) and the relative strength (roughly) of as many resonances as you can for frequencies under 1500 or 2000 hz, and record also the most prominent ones up to 3500 or 4000 Hz.

Now, attempt to identify each resonance by its triple quantum number (Mlmn). You have two major guides here. First, recall that

lmn = .

Using c = 343.4 m/sec., and a = .3 m, b = .4 m, and d = .5 m, you can calculate a table of expected eigenfrequencies for your enclosure.

Secondly, the positioning of your speakers, and the coupling rules given should enable you to generate "selection rules" that rule out certain modes. In general, you will typically find that certain locations prohibit excitation of either even or odd values of l, m, or n.

In the higher frequency ranges, resonances become very closely spaced, and frequently an experiment which changes the speaker placement is the only sure way to resolve an identification.

Once you have gone through this procedure with a simple speaker placement (e.g., along one axis), try another location or orientation. You may have decided in advance by now that some arrangement will favor a predicted set of modes.