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Constantin Fenton

Independent Project:

Investigation on Multiple-Port Loudspeaker Enclosure

Columbia College Chicago

April 30th, 2012

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Introduction

Typical loudspeaker enclosures are usually vented or sealed. The vented enclosures are

commonly fitted with a single port tube that is tuned to a specific frequency of interest. There

have been some investigations on frequency response of vented enclosures with multiple tuned

resonating tubes. [1, 2, 3] i The purpose of this investigation is to measure the frequency response

of a multiple-vent speaker enclosure. This investigation will also attempt to predict the frequency

response of the speaker system mathematically.

The research done by Suzuki et al. [1, 2, 3] demonstrates the mathematics and the

measurements behind different multiple resonating pipe systems. The design that is proposed for

this investigation is a unique four-tube system that attempts to extend the low-end output of an

existing speaker cone in a compact product. This investigation was proposed in order to design

and build a multiple resonating-pipe enclosure according to size requirements by design, and

physical/acoustic principles. The end product of the investigation is a completed prototype, its

response measurement, and an approach to its response prediction.

Calculation

Calculating the response of a speaker system and the effect of the enclosure’s design can

be approached by estimating the characteristic frequencies of the enclosure’s specific chambers,

or tubes. In order to proceed, there are various assumptions that must be made, including those

mentioned in Suzuki’s work. [3, 4] It is important to remember that the application of Suzuki’s

simplified equations to this investigation have been done so under the assumptions included in his

work, and under the assumption that Suzuki’s equations applied to this research are for

approximation purposes. Suzuki’s equations are tailored for a specific multi-pipe resonator in

which the system contains a different sub-chamber for each duct-path; on the other hand, this

investigation focuses on a system with a single main chamber, and that excludes “inter-chamber

ducts”.

The following equations are applied from Suzuki’s equations;

(1)

(2)

(3)

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where,

Spring constant of the chamber (duct) for the mass [N/m]

Ratio of cross sectional area of duct to effective speaker cone area

Effective speaker cone area, used as reference [m2]

Ratio of Specific Heats (=1.40 for air)

Atmospheric Pressure (=90,000, for Mexico City [Pa])

Volume of chamber (duct) [m3]

Mass of involved air in each duct [kg]

Density of air in the duct (=1.062 [kg/m3])

Effective length of the duct [m]

Characteristic frequency of the duct [Hz]

Subscript “j” stands for duct number (tubes 1-4, E.g.: tube1; k1 , tube2; k2 , …tube j; kj )

With the application of the previous equations, it is estimated that tubes 1 and 2, each will

have a characteristic frequency at 82.172 Hz, or 82 Hz. While tubes 3 and 4 are each estimated to

be highly resonant at 112 Hz.

The interaction effects of the repeated frequencies between tubes 1 and 2 for instance, are

difficult to determine since their phase interaction might be more complex to predict. The results

of these interactions are studied in the results section of this report.

Prototype Construction and Evaluation

The prototype was designed with the help of computer design software. The quad-

resonator enclosure features four 2” (4.9 cm dia.) PVC pipes with two different lengths. The pipes

are designed to encapsulate the back wave energy of the low frequency horn, and improve its

low-end output. The system also consists of a main chamber, where energy is distributed. The

quad-resonator’s design can be observed in the following images:

 

 

Figure  2 Figure  1

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The following images show the built prototype of the enclosure system;

The system’s frequency response was tested with an omnidirectional microphone in less than

ideal conditions. The speaker cone used for this research was an Eminence Beta 8-A, an 8”, 8

Ohm cone, with a manufacturer specified resonant frequency of 65hz; which was closely

validated with an electrical impedance test. The following graph (fig. 7) displays the frequency

response measurement of the quad-pipe system. For the purposes of this investigation, the

frequencies of interest will be those below 4,000 Hz. The measurement was made from 20 Hz to

3,500 Hz.

60

70

80

Mag

nitu

de

(dB

)

10 100 1kFrequency (Hz)

Frequency Response (1/12 Octave Smoothing)65.34 @ 92.86

78.84 @ 74.02

71.69 @ 142.66

 Figure  7

Figure  3

Figure  4 Figure  5 Figure  6

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Figure 7 demonstrates how there are strong resonances close to the calculated char.

frequencies; 82Hz and 112 Hz. The graph also shows how the quad-resonator was able to extend

the low frequency response below 78 Hz (manufacturer suggested usable low end range), to 60

Hz. The sharp dips close to the predicted characteristic frequencies could be attributed to complex

phase interactions between the ports and the driver’s front.

Discussion

The results from fig. 7 suggest that that the influence of a quad-resonator enclosure on the

low frequency response of a common speaker cone can be predicted within a certain level

accuracy. In order to complement this research in the future it is recommended that the tubes be

designed to a length that produces a resonance that is directly related to the resonance of the

speaker driver (65Hz).

Also left pending for future studies, is the effect of damping material un the ducts, it

known from Woszczyk’s work [1] that damping material in the duct, such as rock wool or

fiberglass, does in fact reduce the Q factor of the resonance at which a certain tube resonates.

There is great investigation potential for multiple contained-resonating tubes within a

regular shaped enclosure, The mathematics have to be refined and tailored to this specific

application, the Design must be more well developed and built at a higher quality, nevertheless

the overall results suggest that multiple pipe resonators can extend low end response and their

response can be predicted within a certain level of accuracy.

                                                                                                               References

[1] Wieslaw Woszczyk, “A novel Loudspeaker Enclosure and System”, 94th AES Convention, Berlin, March 1993 [2] Shigeru Suzuki, “Equations to Calculate Characteristic Frequencies of Multiple Chamber Aligned in Parallel Cavity Resonator (MCAP-CR)”, http://mcap.web.fc2.com/index.html, revised Nov. 8th, 2008 [3] Mr. Osawa, (first name unknown), “Multiple Pipe Resonator (MPR) Loudspeaker System” online publication released: Jan. 24th 2011 [4] Shigeru Suzuki, “Simplified Method to Estimate Characteristic Frequencies of MCAP-CR ”, http://mcap.web.fc2.com/documents/MCAP006E_simplified-calc.pdf, Nov. 9th, 2008