OverviewWith resonance calculations incorporated into Boxnotes and Sonosub, it seemed like a good idea to check the theory against an experiment. These programs assumed that the driver acted as the open end of a pipe when it came to working out driver-to-wall resonances, predicting a quarter-wave resonance which can spell trouble for tall or deep subwoofers.
The following experiment shows that this premise is false. The driver in fact mimics the closed end of a pipe, leading to half-wave resonances for the driver-to-wall interraction. These are double the frequency of quarter wave resonances, so are better news for subwoofer builders.
The two software products have been corrected as a result of this study.
DesignA 6.5inch woofer was mounted at the end of a 6 inch pipe. At the other end, a baffle with an SPL meter mounted through it, could be moved into the pipe to test different spacings
Testing was done with spacings of 500mm, 400mm and 300mm.
Any half-wave resonances should be visible at 344hz, 430hz and 573hz depending on the spacing used
Any quarter-wave resonances should be visible at 172hz, 215hz and 287hz depending on the spacing used
ResultsThe following graph shows the reults for all three spacings.
As can be seen, the peaks found correspond to multiples of half-wave resonances only.
No evidence of quarter wave resonances is visible.
The result was overlaid on top of the inside measurement for this spacing.
- Red is the original measurement with the SPL meter through the baffle measuring the resonances inside the sub.
- Blue is measured outside the sub, 100mm from the driver.
- Gold is measured outside the sub, 1 metre from driver.
To get a clearer view, here's just the first two, with 1/3 octave smoothing applied.....
- No quarter-wave resonance is seen.
- The first peak is the 1/2 wave resonance around 340hz
- The second peak is the ( 1/2 * 2 ) wave resonance around 680hz
- The third peak is the ( 1/2 * 3 ) wave resonance around 1020hz
- The "dip followed by peak" is presumably due to phase differences as the sweep moves through each of the resonances. The resonance initially interferes with the driver, and as the frequency is raised, comes into reinforcement.
- The intensity has dropped from a 20dB peak inside the box, to a +/- 7dB ripple for the fundamental, and each successive harmonic diminishing by half. Naturally the details would depend on the implimentation, but the principle is there