The golden ratio of 0.618 x 1 x 1.618 will help reduce the effects of standing waves and improve system transience. To apply this ratio to a specific volume of space, simply derive it's cube root and multiply the result by each of the three factors within the ratio.
Example:
Apply the golden ratio to a Vb of 1.5ft^3
• 1.5^(1/3) = 1.447ft or 13.736in
• 13.736 * 0.618 = 8.489in
• 13.736 * 1 = 13.736in
• 13.736 * 1.618 = 22.226in
Therefore, in order for a 1.5ft^3 enclosure to comply with the golden ratio, it's internal dimensions would have to be 8.489in x 13.736in x 22.226in.
To demonstrate how large an impact the internal enclosure geometry has on the overall efficiency curve, here's a graph simulating the infinite environment response of two differently shaped 1.5ft^3 enclosures. Both feature the same driver, the same vent, and the same coordinates along which the woofer and the vent is positioned:
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There are advantages and disadvantages to either approach. For this, let's consider a scenario where the cone area of a single driver is equal to the cumulative cone area of multiple drivers: An example of this would be a single 10" woofer with an Sd of 50in^2 versus a pair of 8" woofers with an Sd of 25in^2 each.
The single driver advantage: Linearity. A single driver system isn't subject to the acoustic or electrical forces countering in phase--even if by a fraction of a degree--which typically occurs when multiple pistons share a common space or when multiple inductors share a common circuit.
The single driver disadvantage: It has been my observation that a single larger driver will typically exhibit higher equivalent air compliance (Vas) than the combined compliance of two smaller drivers. This can translate into higher Vb requirements.
The multiple driver advantage: Assuming that the motor structure is the same on both the 8" and the 10" model, the immediate advantage is twice the motor for every square inch of cone area, twice the power handling, and more end-impedance versatility.
The multiple driver disadvantage: As stated above, using multiple independently actuated pistons increases the risk of the electro-mechanical forces countering one another. This is particularly evident with high Qts drivers.
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Though there are many alignment dynamics responsible for how a speaker sounds, the system's overall performance corresponds to a specific balance of three elements: Efficiency, bandwidth, and size. No matter what the alignment, there's only so far that you can edify any one element without compromising the remaining two: Efficiency describes peak amplitude given set amount of input power, bandwidth describes the response range (low frequency extension, as it applies here,) and size describes the amount of physical space that the enclosure displaces.
Take efficiency, for instance; to improve it, you may have to make the enclosure a bit larger, compromise it's low-end extension, or do a little bit of both. To reduce it's size, you may have to give up some of it's efficiency or bandwidth, and so forth...
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For a practical answer to this question, try listening to a speaker outside of a box, particularly if it's a low-frequency driver. What you're bound to hear is, in part, the air rushing in and out through the vents beneath the spider or the pole vent and, in part, the difference between the two opposing pressures that the cone generates as it moves back and forth.
The purpose of an enclosure is to either confine or alter one of the pressures by means of delay, resonance, or some degree of the two. Both pressures can be manipulated but only one can be confined. If you consider the ratio between the peak output of a speaker operating in free air and that of one mounted within an enclosure, it becomes evident that the enclosure is chiefly responsible for the system's overall efficiency; it's input to output ratio.
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Welcome to the Peter W. Kulicki Knowledge Base; an on-line archive documenting personal discovery and theory that has served me throughout many years of enclosure design. As my ideas evolve, so will this archive, and certain entries may be updated to reflect my latest perspective on a given subject.
What you'll find here is not an exurb from any published technical paper, rather my interpretation of the existing and personally derived theory as it applies to the contemporary listening environment. None of the concepts presented here are indisputably set in stone so please don't e-mail me arguing something that I've written as contradictory to your own perception of the science.
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