An AES Paper Direct Radiator Presented October 27, 1950 Loudspeaker Enclosures HARRY F. OLSON"

A comprehensive analysis of the effect of cabinet configuration on the sound distribution pattern and overall response-frequency characteristics of loudspeakers.

HE PRINCIPAL FACTORS which in- frequency characteristics of a direct- angle a to the pressure for an angle fluence the performance of a direct- radiator louds~eakermechanism a=O. T radiator loudspeaker are the mecha- mounted in the& different housings -- nism itself, the acoustical impedance yield fundamental information regarding I, = Bessel function of the first presented to the back of the mechanism the effect of the outside configuration order, by the enclosure, and the outside con- of the cabinet upon the performance of R = radius of the piston, in centi- figuration of the enclosure. The major this combination. From this study it is meters, portion of the work involving cabinet possible to evolve a cabinet shape which a= angle between the axis of the research, development, and manufacture has the least effect in modifying the piston and the line joining the has been directed towards the acoustical fundamental performance of a direct- point of observation and the impedance presented to the back of the radiator loudspeaker mechanism. center of the piston, and loudspeaker mechanism by the enclosure. A. = wavelength,- in centimeters. The volume of the cabinet and the in- Characteristics of the Sound Source The upper frequency limit for this in- ternal damping means play the most In the experimental determination of vestigation will be placed at 4000 cps. important role in determining the the performance of direct-radiator loud- The reason for selecting this limit is acoustical impedance presented to the speaker mechanisms in various shaped that the enclosures which will be used back of the loudspeaker. In other words, most of the considerations concerning the design of cabinets for direct-radiator loudspeakers have involved the volume or overall dimensions of the cabinet which-together with the mechanism- determines the low-frequency perform- ance. The third factor, namely, the ex- terior configuration of the cabinet, in- fluences the response of the loudspeaker system due to diffraction effects pro- duced by the various surface contours of the cabinet. The diffraction effects are usually overlooked and the anomalies in response are unjustly attributed to the loudspeaker mechanism. Therefore. in order io point up the effects of dif: fraction, it appeared desirable to obtain the performance of a direct-radiator loudspeaker mechanism in such funda- Fig. 2 Direct-radiator loudspeaker mechanism enclosures. The small circle with the dot in mental shapes as the sphere, hemi- the center represents the speaker unit. sphere, cylinder, cube, rectangular parallelepiped, cone, double cone, pyra- enclosures, some consideration must be are relatively large. For example, the mid, and double pyramid. It is the pur- given to the radiating system. These linear dimensions are eight to ten wave- pose of this paper to present the results considerations include the directional lengths at 4000 cps. It will be stipulated of the diffraction studies made upon characteristics of the sound source and that the radiation from the cone of the these fundamental shapes. The response- the sound power output characteristics loudspeaker mechanism at this frequency of the sound source as a function of the shall be down not more than 1.0 db for * RCA Laboratories, Princeton, New frequency. a = 90 deg. as compared to a= 0 deg. Jersey In order to obtain the true diffraction This insures a reasonably nondirectional effects which are produced by the dif- sound source even at the upper end of ferent enclosures, the radiation emitted the frequency range, that is, at 4000 cps. by the sound source must be independent Of course, at lower frequencies the of the direction. Since the diaphragm of response discrepancy with respect to the direct-radiator loudspeaker mecha- angle is much less. To satisfy the above nism used in these tests is relatively very requirements, the diameter of the dia- small, it can be assumed that it is a phragm or cone must be in. Accord- piston source. The directional character- ingly a small direct-radiator loudspeaker istics of a piston source are given by mechanism employing a cone in. in diameter was designed, built, and tested. ~~~(Fsina) A sectional view of the loudspeaker SECTIONAL VIEW mechanism is shown in Fig. 1. Measure- R, = 27rR (1) ments indicated that the directional per- I -sin a fofmance agreed with that predicted by h Fig. 1. Sectional view of the loudspeaker equation (1). mechanism. where R,= ratio of the pressure for an The next consideration is the sound

34 AUDIO ENGINEERING NOVEMBER, 1951 mental resonant frequency .of .the system. . In other words, the performance char- acteristics depicted in.. this paper are, for all practical purposes, the character- MONITORINO RCA-BAI4A RCA-$86 istics which will be obtained if con- LOUDSPEAKER AYPLIEIER - OSCILLATOR ventional direct-radiator loudspeaker mechanisms are used in these enclosures.

Enclosures 4 The encjosures used in these experi- ments are depicted in Fig. 2. The sheet metal sphere shown at (A) is 2 ft. in r I I diameter. The loudspeaker mechanism Is mounted with the cone approximately I FREE FIEU ROOM J L,,, ,-, ,, , , ,,, fludh with the surface. The sheet metal hemisphere shown at (B) is 2 ft. in diameter with the back closed by a flat board of hard wood. The loudspeaker I mechanism is mounted upon the zenith Fig. 3. Schematic diagram of the apparatus for obta~ningthe response-frequency characteristics of the hemisphere with the cone of the of loudspeakers. loudspeaker mechanism approximately flush with the surface. The sheet metal power output calibration of the sound cylinder shown at (C) is 2 ft. in di- source. The sound power output of a ameter and 2 ft. in length. The ends of ,piston sound source radiating into & the cylinder were closed by plywood solid angles and operating in the fre- boards of hard wood. The loudspeaker quency region in which the diameter mechanism is mounted in the center of of the piston is less than one-quarter one end with the cone of the loudspeaker wavelength1 is given by mechanism mounted flush with the sur- face. The cylinder shown at (D) is of the same size as that of (C). In (D) the cone of the loudspeaker mechanism where p= density of air, in gms./cu. cm., is. mounted approximately flush upon c= velocity of sound, in cm./sec., the cylindrical surface midway between a= 2d the ends. The sides of the wood cube f=frequency, in cps, . shown at (E) are 2 ft in length. The S=area of the diaphragm, in sq. loudspeaker mechanism is mounted in cm., the center of one face with the cone i=r.m.s. velocity of the dm- flush with the surface. The base of the phragm, in cm./sec., and Fig. 4. Equipment set-up for obtaining the sheet metal cone shown at (F) is 2 ft. k=r.&.s. +olume current produced response;frequency characteristics of loud- in diameter. The height of the cone is by the mechanism, in cu. cm./ speakers. 1 ft. The base of the cone is closed by Sec. Equation (2) shows that the sound power output PT Of the sound source will be independent of the frequency f, if the velocity &, of the piston is in- versely proportional . to the frequency. The characteristics depicted in this paper have been reduced to 'a sound source of this type, namely, that wh& it radiates into 4n solid angles the sound power output will be independent of the frequency. Since the directivity pattern of the sound source is independent of the frequency, the sound pressure, under these cond'ltions, will also be independent of the frequency. Fig. 5. Microphone It may be mentioned in passing that, and rmpll direct- in the case of a direct-radiator loud- radiator loudspeaker mechanism of Fig. 1 speaker mechanism operating in the under test in the frequency range below the ultimate free-field room. acoustical radiation resistance, the velocity of the cone must be inversely proportional to the frequency in order to obtain constant sound power output, because the acoustical radiation resist- ance is proportional to the square of the. frequency. In order to obtain this type of motion, the system must be mass controlled, which is the natural state of affairs in the direct-radiator type of loudspeaker mechanism above the funds-

. 1 If the upper frequency limit is placed at 4000 cps, the diameter of the %-in. cone- will be less than one-quarter wavelength in the frequency range below 4000 cps. a board of hard wood. The loudspeaker mechanism is mounted in the apex of the FIG. 6 cone. The cone was truncated to ac- I commodate the small loudspeaker mecha- nism. The double cone of (G) consists of two cones, each of the same size as that of the single cone of (F), with the bases placed edge to edge. The loudspeake; mechanism is mounted in the apex of one of the cones. The length of the edges of the square base of the wood FREWNCY IN CYCLES PER SECOND pyramid shown at (H) is 2 ft. The height of the pyramid is 1 ft. The base of the pyramid is closed by a board of hard wood. The loudspeaker mechanism FIG. 8 ED is mounted in the apex of the pyramid. The pyramid was truncated to accom- modate the small loudspeaker mecha- ism. The doublt pyramid of (I) con- sists of two pyramids, each of the same size as that of the single pyramid of (H), with the bases placed edge to edge. The loudspeaker mechanism is mounted in the apex of one of the pyramids. The truncated pyramid of (J) is mounted upon a rectangular parallelepiped. The length of the edges of the truncated FIG. 10 surface is 1 ft. The height of the trun- &rS cated pyramid is 6 in. The lengths of the edges of the rectangular parallele- piped are 1 ft. and 2 ft. The loudspeaker mechanism is mounted in the center of thb truncated surface. The lengths of the *) 0 B edges of the rectangular parallelepiped of w -5 (T() are 2 ft. and 3 ft. The loudspeaker .qechanism is mounted midway between -m,w zoo a00 .oo m .oo amo - ,om rwo two long edges and 1 ft. from one short FREQUENCI IN CYCLES PER YCONO edge. At (L) a rectangular truncated pyramid is mounted upon a rectangular FIG. 13 parallelepiped. The lengths of the edges FIG. 12 of the rectangular parallelepiped are 0 1, 2, and 3 ft, The lengths of the edges of the truncated surface are 1 ft. and 2% ft. The height of the truncated :pyramid is 6 in. One surface of the cpyramid and one surface of the parallele- piped lie in the same plane.

I00 200 MO .w M. U)O '(OO two .- measurement Apparatus and Techniques SECOW - TREWENCV IN CYCLES PER SECOND FREWENCI IN CYCLES PER < The small loudspeaker mechanism of .Fig. 1 was mounted in the enclosures ;shown in Fig. 2. In obtaining true dif- FIG. 14 FIG. 15 .fraction effects it is important that re- +kctiond effects produced by room in ;~hichthe response-frequency character- {tstic is obtained be reduced to a neglig- ~ible minimum. Therefore, all the re- $pnse-frequency characteristics depicted PQ this paper were obtained in the free. deld room2. of the Acoustical Labora- "Qry of the RCA Laboratories. A i,schematic diagram of the apparatus used I FREQUENCY IN CYCLES PER SECOND I I !for obtaining the response-frequency @haracteristics, along with detailed FIG. 16 FIG. 17 gesignations of the components are ~hownin Fig. 3. The complete recording I I %$tern--including the RCA-44B ve- l~citymicrophone, BAlA amplifier, and ;&eeds and Northrup Speedomax re- $order-was calibrated by the free I [Continued on Page 591 i ,- ,- F. J. Acous. Soc. Am., Vol. 100 am sw roo .m .oe low ,ow 8- .mo a zH. Olson, FREQUENCY IN CYCLES PER SECOND FREQUENCY IN CYCLES PER SECOND $6, No. 2, p. 96, 1943. $Olson, Elements of Acoustical En- - - -- girreering, D. Van Nostrand Company, Figs. 6 to 17. Response-frequency characteristic of a small ditect-radiator loudspeaker mecha- @Jew York, 2nd Edition, 1947, p. 359. nism mounted in the enclosures of Fig. 2. 38 AUDIO ENGINEERING NOVEMBER,1951 tion of a small direct-radiator sound primary and diffracted waves are out of source in which the volume current is phase. The minima will occur at 430, LOUDSPEAKER ENCLOSURES inversely proportional to tlie frerluency 860, 1290, etc. cps. It will be seen that and a large spherical enclosure is shown this agrees with the experimental results. in Fig. 6. It will be seen that the re- sponse is uniform and free of peaks and Cylinder field reciprocity metl~od.~?A sinusoidal dips. This is due to the fact that there are The axial response-frequency cl~arac- no sharp edges or discontinuities to set input was applied to the loudspeaker teristicQf the loudspeaker mechanism up diffracted waves of a definite phase of Fig. 1 mounted in the center of one 5y5tem under test by means of the com- pattern relation with respect to the pri- end of the cylinder of (C), Fig. 2 is b i n ati o n RCA-68B beat-frequency mary sound emitted by the loudspealraves are uniformly the intersection of the plane and cylindri- voltage applied to the loudspeaker systein distributed as to phase and amplitude. cal surface introduces a strongly dif- was measured by means of a Ballantine Therefore, the transition from radiation fracted wave. The distance from the voltmeter. The measuring apparatus is by the loudspeaker meclianism into 4p mechanism to the circular boundary is shown in Fig. 4, and the microphone solid angles to radiation into 2T solid 1 it. Tlicl-efore, since the diaphragm and and the small loudspeaker mechanism angles takes place uniformly with re- the edge lie in the same plane, the path of Fig. 1 under test in the free field spect to the frequency. It will be noted difference between primary and dif- that the sound pressure increases uni- iound room are shown in Fig. 5. The fracted wave is 1 it. Followi~ig the forn~lyin this transition frequency. The explanation of tlie preceding section, response-frequency characteristics illus- ultimate pressure is 6 db lligher than there should be luaxinia of response at trated and described in the sections the sound pressure where the climension 550, 1650. 2750, 3550, etc. cps, and there \vhich follo~vwere obtained by means of the sphere is a small fraction of the sl~oultlbe minima of response at 1100, of the apparatus and arrangements de- wavelength. 2200. 3300, etc. cps. It will be seen that xribed above. there is remarkable agreement with the Hemisphere experiniental results of Fig. 8. It is also Sphere interesting to note that the variations The axial response-frequency charac- in response are very great, being of The first consideration will be the teristic of the loudspeaker inecl~anismof the order of 10 clb. combination of the direct-radiator loud- Fig. 1 nlounted in the hemispherical The axial response-frequency charac- 5peaker mechanisni of Fig. 1 and the enclosure of (B), Fig. 2, is shown in teristic of the loudspeaker mechanisin ipherical enclosure as shown at (A) Fig. 7. The sharp discontinuity at the of Fig. 1 tnounted in the cylindrical sur- in Fig. 2. The axial response-frequency boundary of the spherical and plane face of the cylinder of (D), Fig. 2, is surfaces produces a strongly diffracted s11own in Fig. 9. Again the sharp bound- characteristic thus obtained was cor- wave. There is a phase difference be- rected so that the volume current pro- ary between the cylindrical and the plane tween the primary and diffracted waves surfaces produces a diffracted wave. duced by the mechanism was inversely which results in peaks ant1 dips in the proportional to the frequency, as pre- However, the pat11 difference between response-frequency cl~aracteristic cor- tlie primary and diffracted wave is not viously described. The 'esponse-fre- respontling to in and out of phase re- confined to a single discrete distance. quency characteristic6* of the combina- lationships between the primary and Therefore, the maxima and minima of re- diffracted sound. A physical explanation sponse are not as pronounced as in tlie H. F. Olson, RCA Review, Vol. 6, of the phenomena is as follows: The case of (C), as shown in Fig. 8. Fro111 No. 1, p. 36, 1941. sound flows out in all possible directions the response frequency characteristic of 5 Olson, Elements of Acoustical En- from the sound source. The sound which Fig. 9, it would appear that the effective qitzeerilz,q, D. Van Nostrand Company, follows the contour of the spherical distance between the primary and dif- New York, 2nd Edition, 1947, p. 345. surface encounters a sudden change in fracted wave is about 1.17 it. As would The response-frequency characteristics acoustical impedance at the intersection be expected, this means that the forward depicted in tliis paper were obtained on of the plane and spherical surface. A portion of the diffracting edge plays the enclosures having the dimensions given. predominant part. The response-frequency characteristics for reflected wave is sent out at this point in all possible directions. The distance cnclosui-es of other dimensions can be ob- Cube tained by multiplying the ratio of the from the diaphragn~of the loutlspeaker linear ditnensions of the enclosure given in mechanism to the circular diffracting The axial response-frequency cliarac- tliis paper to the linear dimensions of the edge is p/2 feet. The distance between teristic" of tlie loudspeaker mechanism of 1 mounted in the center of one ne\v enclosure by the frequency of the the plane of the diaphragm and the plane Fig. of the faces of the cube (E), of Fig. 2, response-frequency characteristic given in containing circular dlgracting edge is this paper. For example: if the linear is shown in Fig. 10. The sharp boundary 1 ft. Therefore, the difference in path at the edges of the cube produces a dimensions of the new enclosures are two between the primary and the diffracted times those of the enclosures described, the strongly diffracted wave. The average frequency scales of Figs. 6 to 17 inclusive wave at the observation or measure- path between the n~echanism and the should be multiplied by one-half. ment point on the axis is (p/2 + I) ft. The sound wave which follolvs the 7 The theoretical and experimental sound 8 The theoretical and experimental sound pressures on a sphere as a function of the contour of the spherical surface en- pressures on the center of the face of a frequency for an impinging plane wave of counters a decrease in acoustical imped- cylinder as a function of the frequency constant intensity have been investigated ance at the boundary of the spherical have been investigated by Muller, Black by G. W. Stewart, Pkys. Rev., Vol. 33, and plane surfaces, and the diffracted and Dunu, J. Acozls. Sac. Am., Vol. 10, No. 6, p. 467. 1911, S. Ballantine, Phys. No. 1, p. 6, 1938. The results reported by or reflected wave suffers a phase change these investigators agree with those depicted Rev., Vol. 32, No. 6, p. 988, 1928 and Muller, of 180 deg. Therefore, when the distance Black and Dunn, J. Acous. Soc. Am., Vol. in Fig. 8. This is to be expected from a consideration of the reciprocity theoreni. 10, No. 1, p. 6, 1938. The results reported (p/2 + 1) ft. corresponds to odd multi- ples of one-half wavelength, there will Sce footnote 7. hy tticse investigators agree with those de- "The theoretical and experimental sound picted in Fig. 6. This is to be expected be maxima of response because the pri- pressures on the center of a face of a cube from the reciprocity theorem which states mary and diffracted waves are in phase. as a function of tlie frequency have been that under appropriate conditions the source The maxima will occur at 215, 645, 1075, investigated by Muller, Black and Dunn, and observation points may be interchanged etc. cps. It will be seen that tliis agrees J. Arolls. Soc. Ai~z.,Vol. 10, No. 1, p. 6, without altering the response frequency with experimental results. When the 1938. The results reported by these in- characteristics of the systein. See Olson, vestigators agl-ee with those depicted in Blements of Acoustical Engineeritzg, D. distance (p/2 + 1) ft. corresponds to Fig. 10. This is to be expected from a con- Van Nostrand Company, New York, N. Y., n~ultiplesof the wavelength, there will sideration of the reciprocity theorem. See 1947, p. 21. be minima in the response hecause the footnote 7. AUDIO ENGINEERING NOVEM BER, 1951 edges is'about 1.2 ft. Therefore, since frequency characteristicsr; is 6iini'la-f to' mechanism, because of the wide varia- the diaphragm and the edges lie in the that of the cone of a precding secti~n. tions in response produced by diffraction same plane, the path difference between As *in the case of the cone, 't$e ultimate from the sharp edges of this cabinet. the primary and diffracted waves is 1.2 response occurs at a reldtlvely high ft. Following the explanations of the frequency. Rectangirlar Truncated Pyramid and preceding sections, there, should be The axial respolnse of the loudspeaker Parallelepiped Combination maxima of response at 460, 1380, 2300, mechanism of Fig. 1 mounted in the From the data given the preceding 3200, etc. cps, and there should be apex of the double pyramid, (I) of Rig. sections is is possible to devise many minima of response at 920, 1840, 2760, 2, is shown in Fig. 14, The sharp bound- cabinet shapes which will reduce the etc. cps. There is reasonably good agree- ary at the base of the pyramid produces effects of diffractions in modifying the ment with the experimental results of a diffracted wave. The phase differences response frequency characteristics of Fig. 10. between the primary and diffracted the loudspeaker mechanism. waves are the same as those of the single An example of the application of the Cone cone. The performance of the single principles outlined in this paper is shown and double ,cone are about +e$ame, as .at (L) in Fig. 2. In this cabinet the The axial response of the loudspeaker will be seen by comparing Figs. 13 diffraction effects have been ameliorated mechanism of Fig. 1 mounted in the and 14. by the reduction of abrupt angular dis- apex of the cone, (F) of Fig. 2, is shown continuities on the surface of the cabinet in Fig. 11. The sharp boundary at the Truncated Pyramid and Rectangular and the elimination of equal paths from base of th,e cone produces a diffracted Parallelepiped Combination these discontinuities to the mechanism. wave. The distance from the mechanism From the preceding examples, it will At the same time a practical exterior to this edge is 1.3 ft. The distance be- be seen that wide variations in the re- configuration has been retained which is tween the plane of the diaphragm of sponse-frequency characteristics occur not undesirable from an esthetic stand- the mechanism and, the plane of the base when there is a sharp boundary or edge point. The response-frequency charac- is 0.95 ft. Theref~re,the difference in upon the surface of the enclosure which teristic of the loudspeaker n~echanism path between the primary and diffracted produces a strongly diffracted wave. of Fig. 1 mounted in the enclosure (L) waves is 2.25 ft. Following the explana- The diffracted wave is- further accent- is shown in Fig. 17. It will be seen that tions of the preceding sections, there uated when all paths from the mecha- the response-frequency characteristic is should be maxima of response at 250, nism to the boundaries or edges are the quite smooth. 750, 1250, etc. cps. and there should be same. The truncated pyramid and rec- minima of response at 500, 1000, 1500, tangular parallelepiped combination Conclusions ' 2000, etc. cps. There is very good shown at (J) in Fig. 2 is designed with The response-frequency character- agreemenx with the experimental results the object of reducing sharp boundaries istics, which depict the performance of of Fig. 11. Another interesting fact is on -the front portion of the enclosure. a direct-radiator loudspeaker mecha- that the average magnitude of the re- Furthermore, the distances from the nism in various enclosures of funda- sponse does not increase as rapidly with mechanism and the edges are not all the mental shapes, show that the outside frequency as in the case of the examples same. The response frequency charac- ' configuration plays an important part in the preceding sections. This is due teristic of the loudspeaker mechanism in determining the response as a func- to the fact that the free space suhtended of Fig. 1 mounted ifi the enclosure (J) tion of frequency. For example, in some by the loudspeaker mechanism is 2.6 is'shown in Fig. 15. It will be seen that of the enclosures the variation in re- steradians as compared to 2~ steradians the response is quite uniform and free of sponse produced by diffraction exceeds for most bf the other systems considered large maxima and minima. This bears 10 db. in the preceding sections. Therefore, the out the idea that the reduction of sharp All of the response-frequency charac- ultimate sound pressure occurs at a boundaries on the surface of the eh- teristics depicted in this paper were higher frequency than in the case of closure and the elimination of equal path taken on the axis of the loudspeaker enclosures in which the loudspeaker sub- lengths from these boundaries to the mechanism and enclosure combination. tends ZT steradians. mechanism will yield smoother response In this connection, it should be men- The axial response of the loudspeaker frequency characteristics. - tioned that the variations in response are mechanism of Fig. 1 mounted in the mitigated for locations off the axis. The apex of the double cone, (G) of Fig. 2, Rectangular Parallelepiped reason for using the axial response is is shown in Fig. 13. The sharp boundary that the reference response-frequency at the bases of the cones produces a The rectangular parallelepiped in all characteristic of a direct-radiator loud- diffracted wave. The phase differences its possible variations in dimensions is speaker is always taken on or near the between the primary and diffracted the most common direct-radiator loud- axis. Practically all serious listening to waves are the same as those of the single speaker enclosure. One of the obvious direct-radiator loudspeakers is carried cone. The performances of the single reasons for this state of affairs is that out on or near the axis. and double cone are about the same, this !shape is the simplest to fabticate. The response of a loudspeaker in an as will be seen by comparing Figs. 11 This is unfortunate, because the rec- enclosure will be modified by the direc- and 12. tangular parallelepiped produces diffrac- tivity pattern of the mechanism, because \ tion effects which adversely modify the the diffraction effects are influenced by Pyramid response-frequency characteristic of a the direction of flow of sound energy direct-radiator loudspeaker mechanism. from the diaphragm. However, the per- The axial response of the loudspeaker The response-frequency curve of Fig. mechanism of Fig. mounted in the formance in the frequency range in 1 16 was obtained with the toudspeaker which the dimensions of the cone are apex of !he pyramid, (A) of Fig. 2, mechanism of Fig. 1 mounted in the is shown in 13. The sharp boundary less than a wavelength will not be mark- Fig. rectangular parallelepiped of (K), -Fig. edly different. at the base produces a diffracted wave. 2. The pronounced minima in the re- The experiments described in this The average distance from the mecha- sponse at 1000 and 2000 cps are due paper show that the deleterious effects nis~to this edge is 1.6 ft. The distance to shorter distances from the mechanism of diffraction can be reduced by eliminat- 'between the plane of the diaphragm of to the upper and side edges. The mini- ing all sharp boundaries on the front the mechanism and the plane of the base mum in response at 500 cps is due to the portion of the enclosure upon which the is 0.95 ft. Therefore, the difference in longer distance from the mechanism to mechanism is mounted, so that the ampli- path between the primary and diffradted the low& edge. The variations in re- tude of the diffracted waves will be re- waves is 2.55 ft. Following the explana- sponse, due to diffraction eEects by the duced in amplitude and by making the tions of the preceding sections, there cabinet, are of the order of 6 to 7 db. distances from the mechanism to the should be maxima of response at 220, The response frequency characteristic diffracting edges varied so that there 660, 1100, etc. cps, and minima at 440, of Fig. 16 is typical of the response ob- will be a random phase relationship be- 880, 1320, etc. cps. There is very good tained with this' type of enclosure. There- agreement with the experimental results fgre, this cabinet shape is unsuitable for- tween the primary and diffracted sound of Fig. 13. The shape of-the response- housing a direct-radiator loudspeaker' waves. 64 AUDIO ENGINEERING NOVEMBER, 1951