CA1051351A - Cellular sound absorptive structure - Google Patents

Abstract

A B S T R A C T

A sound absorbing structure comprising an orthogonal array of like cells, wherein each cell com-prises a bundle of parallel, terminated, acoustical waveguides. The bundle of waveguides is cut obliquely so that individual waveguides vary substantially in length along the cut. The total admittance of acoustical energy to each absorber cell is the sum of the individual admittances of the waveguides comprising the bundle. The cell (unit bundle) structure is repeated throughout the array. A sound wave arriving at the open end of any cell in the array will encounter at least one waveguide which is effectively resonant at the frequency of the arriving wave. The admittance for the resonant waveguide will be large; the rest of the waveguides will not be resonant to that frequency (admittance is small). The local resonance serves to absorb acoustic energy at its frequency from an area up to about .lambda.2/.pi., where is the wavelength of the sound to be absorbed. Operation of the structure is rela-tively independent of the materials from which it is made and is particularly suitable for sound attentuation in jet engines, high-velocity gas flow ducts, and other applications having similar adverse environmental conditions.

Description

105i351 The present invention relates to a sound absorb-ing structure, and particularly a sound absorbing panel.
Various types of resonant sound absorbers have been proposed heretofore for use in silencers or mufflers S for gas turbine exhaust ducts and similar adverse environ-mental installations. Also, so-called "pan-pipes" type of structures have been proposed heretofore as sound absorbing wall treatments for ducts carrying high velocity gases. The pan-pipe structure comprises a plurality of resonators of diminishing sizes, linearly disposed, to be resonant at var-ious frequencies. While these prior devices may be classi-fied as the same general type of absorber as the present in-vention, namely multiple resonators, their performance is inferior to that of the present invention for reasons that will appear hereinafter.
There is also a honeycomb sandwich type of sound absorption strucutre having an oblique resi~tive partition disposed within each honeycomb cell. In the development of this latter structure it was found that the computed imped-ance p~ots correlated very closely with all empirical data80 long as the resistance of the oblique partition was near optimum or below. However, it was found that beginning with an acoustical resistance somewhat`above optimum, the analyti-cal model failed to predict the experimental results. In this high-resistance region, computer-derived predictions indicated a potentially useful characteristic; namely, an acoustic resistance which increases with frequency and a reactance which rapidly approaches and remains at or near zero. The simple analytical model, upon which th~e computer program for producing the aforementioned impedance plots was

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lOSi351 based, assumed that the basic waveguide was subdivided into a large number (namely, 100) of parallel waveguidelets, each of which functions independently of the others. The total admittance A is, then, the sum of the independent admittances of the waveguidelets, each of which can ba computed from its geometry by classical means.
Thus: A = n An An = z Z = 1 Where: A = Acoustic admittance n = Index num~er (0, 1, 2, 3, etc.) Z = Acoustic Impedance In accordance with the present invention it has been found that experimental data can be made to yield the above-mentioned desired characteristics by physically sub- ~
dividing the cell into 100 (or an appropriately large number ~ -of) waveguidelets.
In the present invention there is disclosed a sound absorptive structure comprising a two-dimensional array (as contrasted with a straight-line or linear array) of contiguous waveguides, open at one end to receive sound waves to be absorbed and of dissimilar lengths. The ratios of the lengths of the several waveguides conform to specified para-meters, so as to provide a wide range of lengths within each funcitonal group or bundle, hereinafter referred to as a cell. Also, the flow resistance of the cell is constrained within prescribed limits for optimum performance, this para-meter being controlled by the geometry of the waveguides, and, in certain cases augmented by a flow-resist~ve facing sheet. Each waveguide is terminated with a reflective lOS1351 termination. Each element of a sound wavefront approaching the array finds at least one waveguide within a surrounding area ~ (viz., "capture area") which is effectively re-sonant at the frequency of its approaching wave. The local resonance serves to absorb the acoustic energy at its fre-quency throughout a capture area of about ~ . This is the basic operating principle of all resonator arrays in the prior art and, of course, this effect occurs in the present invention as well.
It has now been discovered that the sound absorb-ing efficiency and bandwidth of absorption may be substanti-ally improved provided only that certain further geometric constraints are adhered to which assure another additional mechanism of sound absorption. Given one waveguide of length Ll, and hence resonant at some frequency Fl, and a second waveguide of length L2 = 12 Ll, resonant at frequency F2 = 2Fl, then as the frequency is swept from Fl to F2 first the longer waveguide of length Ll will resonate and then ~he second waveguide of length L2 will resonate at frequencies between Fl and F2 such that at their average resonant fre-quency F = F12 2, both waveguides are relatively inactive.
It should be noted at this point that the responses of the two waveguides to the intermediate frequency Fl are opposite in phase relative to the instantaneous sound pressure. If sound pressure strikes the two at the same instant the associated airflow is into one waveguide and out of the other in a "push-pull" manner. This corresponds to the mathematical statement that Zl and Z2 are opposite in sign.
If and only if the two waveguides are sufficiently . .

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close together to assure significant overlap of their cap- -ture area do they interact with each other rather than simply responding slightly and independently to the intermediate sound frequency. If their capture areas overlap then the push-pull phasing in their responses sets up a vigorous ~
local circulation (viz., near field) with an associated sub- ~ -stantial energy absorption to the intermediate frequency sound.
Thus, an important feature of this invention is in part the provision of the geometry required to assure that for virtually every given waveguide, a second waveguide is present within a distance assuring the overlap of their capture areas and thus assuring the substantially increased efficiency of sound absorption.
A sound wave approaching the array finds at least ~-one waveguide within an area = ~ which is effectively re-sonant at the frequency of the approaching wave. The remain-ing waveguides within the area are not resonant to that fre-quency. The local resonance sexves to absorb the acoustic energy at its frequency throughout a "capture area" of up to about ~2/~. Thus, the resonant waveguide effectively serves the entire area. While it is desirable to have the wave-guides as close as possible to each other, practical con-siderations dictate the actual minimum spacing between inter-acting waveguides. As the spacing between interacting wave-guides increases, the overall sound absorption performance becomes progressively degraded. A practical, though some-what arbitrary, limit for the maximum spacing between the two interacting waveguides may be defined as no more than the length of the longer waveguide of the pair. To attain the ~ 051351 required inner geometry the entlre pattern of the array is repeated at frequent intervals glving a striped or checkered appearance and is an essential distinguishing feature between the present invention and the previously-described prior art devices which utillze an assortment of differently tuned resonators distributed in some ar-bitrary manner.
- The present invention provides a sound absorbing panel compr~sing: first and second wavegu~de arrays each compri3ing a plurality of side-by-side acoustical wave-gul~eg of non-uniform length and havlng adjacent ~en ends definlng the sound-receiving end of the array, the sound- , receiving end of like waveguides ln each of said arrays being spaced from each other by a distance not ~ore than .
approximately the wavelength of the sound to be absorbed .
divided by the square root of pls and wavegulde termin-atlng means ~o disposed with re~pect to said waveguides at the ends thereof opposite sald open ends as to result in an àrray of waveguide6 having different lengths and different resonant frequencies.
The pre~ent lnventlon also provldes a sound ab-~orblng structure, comprislng: a plurality of acoustlcal wave~uides having dlssimllar lengths such that ~n ~
(1 - n~)~0, where lo: iB equal to the length of the longest of sald waveguides Qn is the length of the nth waveguide and n is an index number 0, 1, 2, 3, etc~, and ~ is the docrement of length, said waveguides havlng their sound-recelving ends in mutual proximity; and, a plurality of termlnatlng means, equal in number to the number of said waveguldes, each of ., . , , . ...................... ~

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lOS~351 which acoustically terminates a corresponding one of said waveguides at the end thereof away from the sound-receiving end, said plurality of waveguides being disposed with respect to each other in such a way that for any one waveguide of a first given length other than the shortest of said waveguides there is another waveguide approximately half as long as said first gi~en length with its sound-receiving end disposed s~ d ~, with respect to the sound-receiving end of ~a~ one wave-... .
guide, at a center-to-center distance which is not greater than said first given length.
The features and objects of the present invention will be best under~tood from the following description of the accompanying irawings, in which:
FIGURE 1 is a perspective view, partially broken away, illustrating a first preferred embodiment of the in-vention;
FIGURE 2 is a side eleYation view of a second embodiment of the invention employing an internal supporting structuret FIGURE 3 is a side elevation view of a third embodiment of the invention comprising a sound absorptive psnel which is functionally effective on both faces;
FIGURE 4 is a modification fo the apparatus of FIGURE 1 wherein the cells are recessed within individual compaxtments having a common facing sheet;
FIGURE 5 is a network circuit analog of the ~ .
apparatus of FIGURE 4, and FIGURE 6 is a network circuit analog of the ap-paratus of FIGURE 1.
~he present invention comprises a resonant-type absorber which offers an unu~ually wi~e absorption frequency range. As shown in FIGURE 1, a typical embodiment comprise~
a fine honeycomb core structure 1 having proximate bundles of waveguides, each terminated at the closed ends by an oblique partition 2. Each operative unit is enclosed within a group bounded by wall members 3-6 and consists of a bundle (large in number) of parallel acoustical orifices and wave-guides. The bundle of waveguides (1) i8 cut obliquely so that the effective lengths of the waveguides vary along the plane of the cut. The preferred angle of the oblique cut will be discussed more fully hereinafter. A porous or non-porous ~heet or partition 2 i~ located at the plane of the cut. It is required only that the oblique element (2) be sound reflective either by virtue of a high flow resistance, or by being solid, or by virtue of having considerable acoustic impedance. In a practical construction, the struc-ture may include an impermeable backing sheet 7.
Honeycomb core, of conventional and well-known construction, may be used in the fabrication of the wave- ;~
guide9. The core may comprise hexagonal cross-section honeycomb, as shown in FIGURE 1, or may have various other cross-sectional shapes such a~ round, square, triangular, etc. In a typical construction there are a total of 100 waveguides, each 1/8 inch across, located in each group.
Since there is more than one waveguide of each length within the group, in this particular embodiment, the group function-ally may comprise more than one "cell" as previously defined.
In FIGURE 1 wall member 6 is shown as being broken away from the described group in order to expose the const~uction of the internal elements. The depth of the deepest honeycomb ',, . . '. . ' ..': ~ -,'' , - ' .

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core element (e.g., element 8) may, for example, be one inch. A complete cycle of depth (viz., the intergroup spacing) should be located within a similar distance. Be-cause of the "sawtooth" topography of the end-closing parti-tion of the groups, if planned for use as a duct lining,the device may have a preferred orientation relative to the direction of the impinging sound and air flow. Also, the device optionally may be provided with a sound permeable facing sheet 9 for ~tructural, esthetic or other purposes.
The core or honeycomb structure 1 making up the bundle of waveguides may be fabricated from plastic, paper, metal, ceramic, or other suitable material as dictated principally by the intended environment or operation and/or economic constraints. Similarly, the group enclosing walls (e.g., 3-6) and the backing sheet 7 may be made of either metal or non-metallic materials as may be appropriate. The entire structure may be assembled by welding, adhesive bond-ing mechanical interlocking arrangement, or other suitable means. It is the geometry and configuration of the elements that principally determine the operating parameters, rather than the intrinsic properties of the materials from which the device is constructed. Hence, the designer has a wide range of design alternatives with respect to selection of materials for fabrication.
A sound wave approaching the array of differently tuned waveguides (l) will encounter at least one that is resonant, or nearly so, at the frequency (viz., admittance is large). The remaining waveguides within the cell (3-6) are not resonant to that frequency (viz., admittance is small). The local resonance absorbs some of the acoustic lOSi35~

energy at its frequency through an area as large as about ~2/~. For this reason the cell pattern is repeated so as to cover contiguous A2/~ areas. At the lower frequencies a particular waveguide may be resonant for the entire cell by reason of the fact that the cell is dimensioned to be within the aforementioned spacing constraint. Above a frequency roughly double the lowest resonant frequency the capture area ,~ becomes less than the cell area and the resonance mechanism becomes progressively less effective. For the geometry shown in FIGURE 1-4 the length of any two waveguides differ so abruptly that the overlap of thei~ capture areas is apparent within the confines of the cell. The response of any such cell pair to any frequency intermediate between -;
their resonant frequency is of the nature of a push-pull because the shorter one is operating below resonance (Z~ 0) ;
and the longer one is above resonance (z C0).
The resulting vigorous near field leads to vis-cous losses which provide the dissipation of energy needed to attenuate the sound. In thi9 way and by this mechanism the sound absorption remains làrge even at very high fre-quencies for which the actual capture areas have become very small.
The intense near field sonic activity occurring within the waveguides provides the necessary damping for efficient sound absorption even though the terminating plate ~partition 2) is not designed to be permeable. Damping due to scrubbing on the walls of small tubes (l) is proportional to frequency, which helps to explain the increasing acoustic resistance that has actually been observed in practical constructions. ~`
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The oblique element terminating the waveguides (viz., partition 2) should, as has previously been mentioned, be substantially reflective; hence, the reason for a solid partition in a preferred construction. However, this ele-ment may derive its reflectance by virtue of a high flowresistance, or by having considerable acoustic inertance.
For example, an oblique termination operating as a high-inertance mechanism may comprise a foraminous plate having a small percentage of open area. This would yield the re-quired reflectance, but would desirably provide liquiddrainage to each waveguide as may be required in certain types of installations.
In the embodiment of FIGURE 1, the group enclosure comprising wall members 3-6 is shown to have a square cross section. This shape is arbitrary. If desired, the boundar-ies of a cell or group of cells may, as in the case of the waveguides, have any desired cross-sectional shape such as hexagonal, round, triangular, rectangular, etc. The princi-pal operating parameter with respect to the configuration of the cell is that it have a maximum over-lapping of capture areas between as many waveguide pairs as possible. Also, the construction shown in FIGURE 1 employs an ob}ique planar partition 2 for terminating the plurality of waveguides within the corresponding cell. As will be appreciated, partition 2 need not be planar since other surface configura-tions such as conical, exponential, etc., could be utilized and still yield the necessary differences in depth of the several nearby waveguides. The essential consideration is that the bundle of waveguides be terminated in s~ch a manner that the depths of the several waveguides vary through a ~ 05135~
range of dimensions sufficiently wide to accommodate the sound spectrum of interest.
In order to obtain the desired area overlap or "capture effect" of the close1y-spaced waveguides, it is necessary to have at least one waveguide within each cell which is below resonance and one above resonance at the fre-quency of the incoming wave. To assure this, the ratio of length of the longest waveguide to that of the shortest wave-guide should be as high as possible. That is, the rate of change of waveguide length (the slope of oblique partition 2) is an important parameter. Sufficient slope improves ;
performance and permits the use of coarser, larger cell sizes. Since each waveguide has an effective sound-receiving area that is greater than its actual cross-sectional area, -~
the waveguides comprising each cell should be so tightly packed that the "effective" area of any waveguide at reson- -~
ance always overlaps the effective areas of any other wave-guide at antiresonance. This is accomplished by varying the lengths of the waveguides within the cell abruptly. This is assured if the angle of elevation of the partition 2 is at least 45. Below 45, the resonators take increasingly independent operating (viz., non-parallel) characteristics, and performance deteriorates. For angles greater than 45, little further improvement occurs at the lower frequencies, but some further improvement occurs at very high frequencies.
The invention operates because the differing waveguides are not only tuned to different resonant fre-quencies, but also because they act with predetermined phase relationships. Specifically, they are spaced closely enough to permit phased interaction rather than independent iO5135~
operation.
Any resonator undergoes a rapid phase shift of the oscillating flow relative to the pressure wave as the frequency passes from below resonance to above resonance.
If the damping is relatively light, this phase shift amounts to nearly 180 degrees. Thus, given two widely spaced apart resonant tubes, one of which is twice the length of the other, at any given frequency between the two first resonant frequencies the flow will be entering the first tube and will be leaving the second tube at a particular instant in time. I e the two tubes are placed close enough together, their effective areas will overlap. To assure this, the center-to-center distance between the tubes must be reduced to approximately one-quarter wavelength of the resonant fre-quency of the shorter tube. Since one tube is only half thelength of the other, the angle between the common entrance plane of the pair of tubes and that of the closed ends of the tubes is about 45. If this angle is much less than 45 the geometry requires that they be more widely spaced apart and the consequence is that they will act independently.
If, on the other hand, the effective areas of the -two resonators overlap, a vigorous interaction occurs and they no longer act independently, but rather are said to act in parallel coupling. At frequency Fl, the first tube is resonant and the second tube quiescent, and conversely. At frequency F = F12+ F2 a resonant-like condition exists in-volving a strong local circulation between the two tubes.
This is called a "near field." This vigorous near field local circulation into and out of both tubes results in much greater acoustical energy absorption than the combined effect . ~

~OS1351 of the resonators acting independently at frequency F because neither is resonant by itself at F.
To assure the desired parallel coupling with practically realizable geometries, while maintaining the necessary small inter-cell spacing, requires that the ratio of the depths of the shortest waveguide to the longest wave-guide in any given cell be quite large (i.e., equal to or greater than 1:2). This corresponds to a large diagonal slope (i.e., ~30) of the plane through the closed ends of the waveguides).
Other structural modifications may be made to provide load-bearing properties or other characteristics dictated by the intended operating environment. For example, there is shown in FIGURE 2 a cross-sectional elevation view of a resonant type sound absorber panel constructed in accordance with the invention, having potentially greater structural strength than the configuration of FIGURE 1.
This embodiment c~mprises a non-porous backing sheet 11 and a substantially sound transparent facing sheet 12. Cell enclosing walls 13 and 14 are perpendicularly disposed be-tween mutually confronting backing sheet 11 and spaced apart facing sheet 12. The bundle of waveguides within each cell is fabricated from an integral honeycomb core element. In the course of manufacture of the panel, the honeycomb core element for each cell is first cut on a bias so as to divide the element into an upper and lower section 15 and 16, re-spectively. The reflective terminating partition 17 is then interposed between the upper a~d lower sections 15 and 16. i The operative, sound absorbing, section lS is exposed to the incoming sound wave through sound-transparent facing : ' . . .

she~t 12. The lower section 16 serves primarily to support the partition 17 and lend structural rigidity to the overall device. Also, this construction minimizes the requirements for attaching or otherwise securing the partition and the waveguide members to the adjoining cell-defining members.
Again, it is not necessary that the partition 17 be a planar oblique element since it could have a curved, angular, or other compound shape, as desired, to vary the effective depth of the tubular sound-receiving portions of the honeycomb ele-ment 15.
There is shown in FIGURE 3 yet another embodimentof the invention which is characterized by having two sound absorbincJ faces. This embodiment is generally similar to that of FIGURE 2 and comprises group-defining wall members 18 and 19, and upper and lower honeycomb core sections 21 and 22, respectively. The core sections 21 and 22 are separated by an interposed sound reflective partition 23.
Unlike the construction of FIGURE 2 (which has a non-porous backing sheet 11), the embodiment of FIGURE 3 is provided with separate sound transparent sheets on both sides of the panel. That is, the waveguide bundle comprising upper sec-tion 21 is covered by sound transparent sheet 24, and the waveguide bundle comprising lower section 22 i9 covered by sound transparent sheet 25. Since the panel structure i8 symmetrical about its central axis 26, sound approaching either side of the panel will be absorbed. As in the case of the previously described embodiments, the topography of the partition that reflectively terminates the waveguide may be either planar or curved as desired.
There is shown in FIGtlRE 4 an alternative 10513Sl embodiment of the invention. This construction comprises a plurality of cell groups each enclosed on four sides. Typi-cal wall members enclosing the sides of the cell groups are indicated at 32 and 33. It should be understood that the two remaining wall members (not shown in FIGURE 4) for the cells bounded by members 32 and 33 are orthogonally disposed thereto in order to form a four-sided cell group having a square cross sectlon. This square shape is arbitrary and i8 by way of example only. A bundle of waveguides 31 is located within the cell group. The open, sound-receiving, ends of the waveguides (31) are at the top of the cell group, as viewed in FIGURE 4. A solid wall member 34 closes the bottom ends of the cell groups. An oblique planar partition, such as that indicated at 35, terminates the plurality of wave-guides within each cell. A permeable facing sheet 36 ex-tends across the open ends of all of the cell groups.
As can be seen, the depth of the cell groups is greater than the depth of the longest waveguide disposed therein, thereby providing an open area or cavity 37 between - 20 the sound receiving ends of the waveguides and the permeable facing sheet 36. That is, the bundle of waveguides 31 is recessed within the cell cavity 90 as to be spaced apart from the facing sheet 36. Functionally, the facing sheet 36 i5 common to all of the cells comprising the array, and operates as a series acoustical resistance for the entire array. This arrangement provides a slightly different ab- -sorption spectrum shape than would be obtained without the cavity 37. The configuraiton shown in FIGURE 4 is preferred where it is desired that a coarse perforate be used having holes comparable to the diameter of the waveguide entrances.

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,, : ~ '~ : . , '' . , 10~1351 To facilitate a comparison between these two embodiments of the invention there is shown in FIGURES 5 and 6 electrical network analogs which correspond to the acoustical apparatus of FIGURE 4 and FIGURE 1, respectively.
Referring first to FIGURES 4 and 5 there is shown the electrical network equivalent of the apparatus of FIGURE
4 wherein terminal 3a comprises the input to the device, and serie~ resistance 39 corresponds to the acou~tical resistance of the facing member 36. The capacitive reactance, and the wall-scrubbing resistance of each cell in the array (as pro-vided by the then-active waveguide within each cell) is represented by a series capacitance and resistance. For example, the active waveguide in the first cell corresponds to capacitance 41 and resistance 45, the next cell corre-sponds to capacitance 42 and resistance 46, and 80 forth throughout the parallel array comprising branch capacitances 41-44 and series resistances 45-48. The network is refer-enced to ground terminal 49.
As can be seen, resistance 39 (and hence the flow resistance of facing sheet 36) is in series with the parallel combination of all of the capacitances 41-44 and resistances 45-48 (which correspond to the overall array).
The network of FIGURE 6 corresponds to the appara-tus of FIGURE 1 and is provided with an input terminal 51.
Resistances 52-55 correspond to the resistances of the in-dividual areas of the facing sheet 9 which extend over the open area of each individual waveguide within a cell. Capac-itances 56-59 correspond to the acoustical capacitive reac-tances of corresponding waveguides, and resistances 61-64 correspond to the scrubbing resistances of corresponding ~OS1351 waveguides. The network is referenced to ground 65.
Certain precautions must be taken with respect to obtaining valid result~ from the foregoing network analogs.
The parallel waveguide~ can be represented by their parallel circult elements only if the waveguides are packed so closely that they act in parallel ~i.e., if their capture areas overlap such that they act in parallel rather than indepen-dently). Acoustic resistance~ and reactances must be ex-pressed in units of acoustical ohms to be analogous to elec-trical ohms.
The acousitc reactance of the waYeguide is in reality of the form: X = -; cot c~ L and is approximated by a capacitance only at low frequencies.
In summary, the present invention, in all embodi-ments, comprises a parallel-coupled system because of the close constraint of the inter-cell spacing and because of the wide range of depths of the waveguides, whereby the effective areas of the waveguides at resonance always over- ~-lap with the area~ of other waveguides at anti-resonance.
Other modifications may be made in order to ~ccommodate particular applications. For example, the over-all structure may have a curved shaped (as contrasted with planar facing or bàcking sheets) as may be required for lining a circular duct or other curved boundary. Also, the facing sheets may be omitted without impairing the sound ab~orptive properties of the device. Still other modifica-tions may be made by tho~e versed in the art without depart-ing from the invention-as set forth above.

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Claims (9)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. A sound absorbing panel comprising: first and second waveguide arrays each comprising a plurality of side-by-side acoustical waveguides of non-uniform length and having adjacent open ends defining the sound-receiving end of the array, the sound-receiving end of like waveguides in each of said arrays being spaced from each other by a distance not more than approximately the wavelength of the sound to be absorbed divided by the square root of pi;
and waveguide terminating means so disposed with respect to said waveguides at the ends thereof opposite said open ends as to result in an array of waveguides having different lengths and different resonant frequencies.

2. A sound absorbing panel as defined in claim 1 including an imper-meable backing sheet disposed adjacent the ends of said waveguides opposite said open ends, said terminating means being disposed between said ends of said waveguides opposite said open ends and said backing sheet.

3. A sound absorbing panel as defined in claim 1 or 2, including a sound-transparent facing sheet overlying the sound-receiving ends of said arrays.

4. A sound absorbing panel as defined in claim 1 or 2, including a permeable, flow-resistive, facing sheet spaced apart from and extending across the sound-receiving ends of said arrays.

5. A sound absorbing panel as defined in claim 1 or 2, wherein each of said waveguides has an hexagonal cross-section.

6. A sound absorbing panel as defined in claim 1 or 2, wherein each of said arrays has a square cross-section.

7. A sound absorbing panel as defined in claim 1 wherein said terminat-ing means is provided by a planar impermeable sheet closing like ends of the waveguides comprising each array.

8. A sound absorbing panel as defined in claim 7, wherein said planar impermeable sheet is disposed at an angle with respect to said sound-receiving end of the array, which is ? 30°.

9. A sound absorbing panel as defined in claim 1, wherein an array comprises a plurality of acoustical waveguides having dissimilar lengths such that ?n = ?? - n ???, where ?? is equal to the length of the longest of said waveguides, n is the length of the nth waveguide and n is an integer, and ??? is the decrement of length, said waveguides having their sound-receiving ends in mutual proximity, and, waveguide terminating means for acoustically terminating said waveguides at the ends thereof away from the sound-receiving ends, said plurality of waveguides being disposed with respect to each other in such a way that for any one waveguide of a first given length other than the shortest of said waveguides there is another waveguide approximately half as long as said first given length with its sound-receiving end disposed with respect to the sound-receiving end of said one waveguide, at a center-to-center distance which is not greater than said first given length.