`
`
`EXHIBIT 2009
`
`EXHIBIT 2009
`
`

`

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`
`
`
`THX Ltd. Exhibit 2009 Page 1
`|PR2014-00235
`
`THX Ltd. Exhibit 2009 Page 1
`IPR2014-00235
`
`

`

`-~ I !
`
`i
`
`. i
`;
`
`
`
`ACOUSTICS
`ACOUSTICS
`
`
`
`THX Ltd. Exhibit 2009 Page 2
`|PR2014-00235
`
`THX Ltd. Exhibit 2009 Page 2
`IPR2014-00235
`
`

`

`ACOUSTICS
`
`LEO L. BERANEK
`
`Acomtics Laboratory, Massachmetts Institute
`of Technology; Bolt, Beranek and Newman, Inc.,
`Cambridge, M assachmetts
`
`McGRAW-HILL BOOK COMPANY,
`
`New York
`
`Toronto
`
`London
`
`1954
`
`THX Ltd. Exhibit 2009 Page 3
`IPR2014-00235
`
`

`

`ACOUSTICS
`
`Copyright, 1954, by the McGraw-Hill Book Company, Inc. Printed in the
`United States of America. All rights reserved. This book, or parts thereof,
`may not be reproduced in any form without permission of the publishers.
`
`Library of Congress Catalog Card Number 53-12426
`
`11121314-MP - 9
`
`04835
`
`PREFACE
`
`Acoustics is a most fascinating subject. Music, architecture, engineer(cid:173)
`ing, ~~ience, drama, medicine, psychology, and linguistics all seek from it
`In the Acoustics Laboratory
`answ~ers to basic questions in their fields.
`at ·M.I.T. students may be found working on such diversified problems
`as auditorium and studio design, loudspeaker design, subjective percep(cid:173)
`tion of complex sounds, production of synthetic speech, propagation of
`sound in the atmosphere, dispersion of sound in liquids, reduction of noise
`from jet-aircraft engines, and ultrasonic detection of brain tumors. The
`a~ual meetings of the Acoustical Society of America are veritable five(cid:173)
`ring shows, with papers and symposia on subjects in all the above-named
`fields. Opportunities for employment are abundant today because man(cid:173)
`agement in industry has recognized the important contributions that
`acoustics makes both to the improvement of their products and to the
`betterment of employee working conditions.
`There is no easy road to an understanding of present-day acoustics.
`First the student must acquire the vocabulary that is peculiar to the
`subject. Then he must assimilate the laws governing sound propagation
`and sound radiation, resonance, and the behavior of transducers in an
`acoustic medium. Last, but certainly not of least importance, he must
`learn 'to understand the hearing characteristics of people and the reac(cid:173)
`tions of listeners to sounds and noises.
`This book is the outgrowth of a course in acoustics that the author
`has taught to seniors and to first-year graduate students in electrical
`engineering and communication physics. The basic wave equation and
`some of its more interesting solutions are discussed in detail in the first
`part of the text. The radiation of sound, components of acoustical sys(cid:173)
`tems, microphones, loudspeakers, and horns are treated in sufficient detail
`to allow the serious student to enter into ehktroacoustical design.
`There is an extensive treatment of such important problems as sound
`in enClosures, methods for noise reduction, hearing, speech 'intelligibility,
`and psychoacoustic criteria for comfort, for satisfactory speech intelligi(cid:173)
`bility, and for pleasant listening conditions.
`The bpok differs in one important respect from conventional texts on
`acoustics in that it empha~izes the practical application of electrical(cid:173)
`'Wherever
`circuit theory in the solution of a wide variety of problems.
`possible, the background of the electrical engineer and the communica(cid:173)
`tion physicist is utilized in explaining acoustical concepts.
`
`THX Ltd. Exhibit 2009 Page 4
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`

`

`206
`
`DIR E CT - R ADI ATO R L OU D S PEA K ERS
`
`[Chap. 7
`
`about 0.5 sec, which corresponds to a decay constant of 13.8 sec- 1•
`Psychological studies also indicate that if a transient sound in a room has
`decreased to less than 0.1 of its initial value within 0.1 sec, most listeners
`are not disturbed by the" overhang" of the sound. This corresponds to
`a decay constant of 23 sec-1, which is a more rapid decay than occurs in
`the average living room. Although criteria for acceptable transient dis(cid:173)
`tortion have not been established for loudspeakers, it seems reasonable to
`assume that if the decay constant for a loudspeaker is greater than fbui:
`times this quantity, i.e., greater than 92 sec-t, no serious objection will be
`met from most listeners to the transient occurring with a tone burst.
`Accordingly, the criterion that is suggested here as· representing satis(cid:173)
`factory transient performance is
`RM -- > 92 sec- 1
`2MM
`Equation (7.35) reveals that, the greater RM/2MM, the shorter t he
`transient. E quation (7.39) should be construed as setting a lower limit
`on the amount of damping that must be introduced into the system. It
`is not known bow much damping ought to be introduced beyond this
`minimum amount.
`In the next chapter we shall discuss t he relation between t he criterion
`of Eq. (7.39) and the response curve with baf!l.e.
`Each of t he diaphragm resonances (e.g., points 1 to 8 in Fig. 7.8) has
`associated with it a transient decay t ime determined from an equation
`like Eq. (7.35).
`I n order to fulfill the criterion of Eq. (7.39), it is usually
`necessary to damp the loudspeaker cone and to terminate t he edges so
`that a response curve smoother than that shown in Fig. 7.8 is obtained.
`With the very best direct-radiator loudspeakers much smoother response
`curves are obtained. The engineering steps and the production control
`necessary to achieve low transient distortion and a. smooth response curve
`may result in a high cost for the completed loudspeaker.
`
`(7.39)
`
`If the circular gap in t he permanent magnet has a radial length of
`Example 7.3.
`0.2 em, a circumference of 8 em, and an axial length of 1.0 em, determine the energy
`stored in the air gap if the flux den.sity is 10,000 gauss.
`Solution.
`
`Volume of air gap = (0.002)(0.08)(0.01) = 1.6 X IO- • m•
`Flux density = 1 weber jm•
`From books on magnetic devices, we find that the energy stored is
`B•V
`W = -
`-
`2~"
`where the permeability I' for air is l'ri = 4,- X IQ-7 weber /(amp-turn m). Hence, the
`air-gap energy is
`
`(1)(1.6 X IO-•) = ~ = 0.636 joule
`W = oM - .
`• ~ "
`
`, .
`
`"
`
`Part XVIII]
`
`D ESIGN FACTORS
`
`207
`
`Example 7.4. A 12-in. loudspeaker is mounted in one of the two largest sides of a
`closed box having the dimensions 27 by 20 by 12 in. Determine and plot t he relative
`power available efficiency and the relative sound pressure level on the principal axis.
`Solution. Typical directivity patterns for this loudspeaker are shown in Fig. 4.23.
`The directivity index on the principal axis as a function of frequency is shown in Fig.
`4.24. It is interesting to note that the transition frequency from low directivity to
`high directivity is about 500 cps. Since the effective radius of the radiating cone for
`this loudspeaker is about 0.13 m, ka at this transition frequency is
`
`ka = 2r.fa = 1000r. X 0.13
`344.8
`c
`
`= 1.18
`
`or nearly unity, as would be expected from our previous studies. The transition from
`region C [where we assumed that w 2M M 12 » lRMR2 and w2L 2 « (R. + Re)2] to region E
`of Fig. 7.6 also occurs at about ka = 1.
`In the frequency region between ka = 0.5 and ka = 3, the loudspeaker can be
`represented by the circuit of Fig. 7.4a. Let us assume that it is mounted in an infinite
`baffie and that one-half the power is radiated to each side. Also, let us assume that
`the amplifier impedance is very low.
`The power available efficiency, from ~me side of th.e loud$peaker, is
`PAE, = w, =
`400B•l•R. lRMR -
`(R. + Re)'(RMT' + XJCT2 )
`W e
`•LZ
`where
`+ (RMs + 2mMR) ..J1 + R w+ Re
`B•z•
`=
`R
`v(R. + Re)• + w•L•
`•
`MT
`wLB2l2
`•£>
`X MT = (wMMD + 2XMR) ...}1 + (R w~ Re)• -
`(R + Re)• v 1 + [w2L'/(R. + Re)']
`•
`•
`(7.42)
`
`(7.41)
`
`(7.40)
`
`If we assume the constants for Example 7.2, we obtain the solid curve of Fig. 7.15a.
`It is seen that, abovef = 1000 cps, the power available efficiency drops off.
`
`10
`"'
`~~
`"2 ~ 5
`-~~ 0
`ge
`g.:E -5
`a::"' - 10
`200
`
`"0~
`
`.,~
`
`-
`
`\ S.P.L
`I _ :l-~
`~
`L P.A.E.
`
`5
`6 7 8 91000
`Frequency in cycles per second
`Fro. 7.15. Graphs of the relative power available efficiency and the sound pressure
`level measured on the principal axis of a typical 12-in.-diameter loudspeaker in a
`closed-box baffle. The reference level is chosen arbitrarily.
`
`2000
`
`Now, let us determine the sound pressure level on the principal axis of the loud(cid:173)
`speaker, using Eq. (7.34). The directivity index for a·piston in along tube is found
`from Fig. 4.20. The results are given by the dashed curve in Fig. 7.15. Obviously,
`the·directivity index is of great value in maintaining the frequency response on the
`principal a..xis out to higher frequencies. At still higher frequencies, cone resonances
`occur, as we said before, and the typical respon.se curve of Fig. 7.8 is obtained.
`
`THX Ltd. Exhibit 2009 Page 5
`IPR2014-00235
`
`

`

`CHAPTER 8
`
`LOUDSPEAKER ENCLOSURES
`
`PART XIX Simple Enclosures
`
`Loudspeaker enclosures are the subj.ect of more controversy than any
`other item connected with modern high-fidelity music reproduction.
`Because the behavior of enclosures has not been clearly understood, and
`because no single authoritative reference has existed on the subject,
`opinions and pseudo theories as to the effects of enclosures on loudspeaker
`response have been many and conflicting. The problem is complicated
`further because the design of an enclosure should be undertaken only with
`full knowledge of the characteristics of the loudspeaker and of the
`amplifier available, and these data are not ordinarily supplied by the
`manufacturer.
`A large part of the difficulty of Selecting a loudspeaker and its enclosure
`arises from the(fact that the psychoacoustic factors invoived in the repro(cid:173)
`duction of · speech and music are not understood. Listeners will rank(cid:173)
`order differently four apparently identical loudspeakers placed in four
`identical enclosures. It has been remarked that if one selects his own
`components, builds his own enclosure, and is convinced he has made a wise
`choice of design, then his own loudspeaker sounds better to him than does
`anyone else's loudspeaker. In this case, the frequency response of the
`loudspeaker seems to play only a minor part in forming a person's
`opinion.
`In this chapter, we shall discuss only the physics of the problem. The
`designer should be able to achieve, from this information, any reasonable
`frequency-response curve that he may desire. Further than that, he will
`have to seek information elsewhere or to decide for himself which shape
`of frequency-response curve will give greatest pleasure to himself and to
`other listeners.
`·
`With the information of this chapter, the high-fidelity enthusiast should
`be .able to calculate, if he understands a-c circuit theory, the frequency(cid:173)
`response curve for his amplifier-loudspeaker-baffle combination. Design
`208
`
`Part XIX]
`
`SIMPLE. ENCLOSURES
`
`209
`
`A
`
`graphs are presented to simplify the calculations, and three complete
`examples are worked out in detail. Unfortunately, the calculations are
`sometimes tedious, but there is no short cut to the answer.
`As we have stated earlier, all calculations are based on the mks system.
`A conversion table is given in Appendix II that permits ready conversion
`from English units. The advantage of working with meters and kilograms
`is that all electrical quantities may be expressed in ordinary watts, volts,
`I t is believed that use of the mks system leads to
`ohms. and amperes.
`less confusion than use of the cgs system 1 where powers are in ergs per
`second, electrical potentials are volts X lOS, electrical currents are
`amperes X I0-1, and impedances are ohms X 109•
`8.1. Unbaffied Direct-radiator Loudspeaker. A baffle is a st ructure
`for shielding the front-side radiation of a loudspeaker diaphragm from
`the rear-side radiation. The necessity
`for shielding the front side from the rear
`side can be understood if we consider
`that an unbaffied loudspeaker at low
`frequencies is the equivalent of a pair of
`simple spherical sources of equal strength
`located near each other and pulsing out
`of phase (see Fig. 8.1). The rear side of
`FIG. 8.1. Doublet sound source
`the diaphragm of the loudspeaker is
`equivalent at low frequencies to
`equivalent to one of these sources and
`an unb~tiied :'ibrat ing diaphragm.
`The pomt A lS located a d1stance r
`.
`.
`.
`'
`the front mde 1s eqwvalent to the other.
`and at an angle 8 with respect to
`If we measure, as a function of fre-
`the axis of the loudspeaker.
`quency f, the magnitude of the rms
`·
`sound pressure pat a point A, fairly well removed from these two sources,
`and if we hold the volume velocity of each constant, we find from Eq.
`(4.15) that
`
`0
`
`-1 b J(cid:173)
`
`rc
`
`(8.1)
`
`where U0 = rms strength of each simple source in cubic meters per
`second.
`b = separation between the simple sources in meters.
`Po = density of air in kilograms per cubic meter (1.18 kg/ m3 for
`ordinary temperature and pressure).
`r = distance in meters from the sources to the point A . It is
`assumed that r » b.
`8 = angle shown in Fig. 8.1.
`c = speed of sound in meters per second (344.8m/sec, normally).
`
`1 II. F . Olson, "Elements of Acoustical Engineering," 2d ed., pp. 84-85, Table 4.3,
`D. Van Nostrand Company, Inc., New York, 1947. For a discussion of simple
`loudspeaker enclosures, see pp. 144-154.
`
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`IPR2014-00235
`
`

`

`210
`
`LOUDSPEAKER ENCLOSURES
`
`[Chap. 8
`
`In other words, for a constant-volume vefocity of the loudspeaker dia(cid:173)
`phragm, the pressure p measured at a distance r is proportional to the
`square of the frequency f and to the cosine of the angle 9 and is inversely
`In terms of decibels, the sound pressure p increases at
`proportional to r.
`the rate of 12 db for each octave (doubling) in frequency.
`In the case of an actual unbaffled loudspeaker, below the first resonance
`frequency where the system is stiffness-controlled, the velocity of the
`diaphragm is not constant but doubles with each doubling of frequency.
`This is an increase in velocity of 6 db per octave. Hence, the pressure p
`from a loudspeaker without a baffle increases 12 + 6 = 18 db for each
`octave increase in frequency. Above the first resonance frequency,
`where the system is mass-controlled, the velocity of the diaphragm
`decreases 6 db for each octave in frequency. Hence, in that region, the
`pressure p increases 12 - 6 = 6 db for each octave increase in frequency.
`8.2. Infinite Baffle.
`In the previous chapter we talked about direct(cid:173)
`radiator loudspeakers in infinite baffles. Reference to Fig. 7.6 reveals
`that \vith an infinite baffle, the response of a direct-radiator loudspeaker
`is enhanced over that just indicated for no baffle. It was shown that if
`one is above the first resonance frequency usually the response is flat with
`frequency unless the Bl product is large (region C) and that if one is below
`the first resonance frequency the response decreases at the rate of 12 db
`per octave instead of 18 db per octave. Hence, the isolation of the front
`side from the back side by an infinite baffle is definitely advantageous.
`In practice, the equivalent of an infinite baffle is a very large enclosure,
`well damped by absorbing material. One practical example is to mount
`the loudspeaker in one side of a closet filled with clothing, allowing the
`front side of the loudspeaker to radiate into the adjoining listening room.
`Design charts covering the performance of a direct-radiator loudspeaker
`in an infinite baffle are identical to those for a closed-box. We shall
`present these charts in Par. 8.5.
`8.3. Finite-sized Flat Baffle. The discussion above indicated that it
`is advisable to shield completely one side of the loudspeaker from the
`other, as by mounting the loudspeaker in a closet. Another possible
`alternative is to mount the loudspeaker in a fiat baffle of finite size, free
`to stand at one end of the listening room.
`The performance of a loudspeaker in a free-standing fiat baffle leaves
`much to be desired, however. If the wavelength of a tone being radiated
`is greater than twice the smallest lateral dimension of the baffle, the loud··
`speaker will act according to Eq. (8.1). This means that for a finite flat
`baffle to act approximately like an infinite baffle at 50 cps, its smallest
`lateral dimension must be about 3.5 m (11.5 ft). However, even above
`this frequency, sound waves traveling from behind the loudspeaker reflect
`off walls and meet with those from the front and cause alternate cancella(cid:173)
`tions and reinforcements of t he sound as the two waves come into phase or
`
`----
`
`SIMPLE ENCLOSURES
`
`211
`
`Part XIX)
`out of phase at particular frequencies in particular parts of the room.
`This effect can be reduced by locating the loudspeaker off center in the
`baffle, but it cannot be eliminated because of reflections from the walls of
`the room behind the loudspeaker. Also, a fiat baffle makes the loud(cid:173)
`speaker more directional than is desirable because in the plane of the
`baffle the sound pressure tends to reduce to zero regardless of the baffle
`size.
`8.4. Open-back Cabinets. An open-back cabinet is simply a box with
`one side missing and with the loudspeaker mounted in the side opposite
`the open back. Many home radios are of this type. Such a cabinet
`performs nearly the same as a flat baffie that provides the same path
`length between the front and back of the loudspeaker. One additional
`
`r/
`LLU
`L
`·~
`
`c"
`
`2
`Flo. 8.2. Loudspeaker of radius a
`mounted in a.n unlined box with
`dimensions L X L X L/2. While
`this type of box is convenient for
`analysis, the construction shown in
`Fig. 8.3 is more com.monly used.
`
`:q:;;,
`
`Plywood
`0.7 to 1.0 inch .
`thick
`
`Acoustical lining
`0.5 to 1.5 inch
`thick
`
`FIG. 8.3. Typical plywood box with
`loudspeaker mounted off center in one
`side and lined with a layer of soft ab(cid:173)
`sorbent acou:;tical material.
`
`effect, usually undesirable, occurs at the frequency where the depth of the
`box approaches a quarter wavelength. At this frequency, the box acts
`as a resonant tube, and more power is radiated from the rear side of the
`loudspeaker than at other frequencies. Furthermore, the sound from
`the rear may combine in phase with that from the front at about this
`same frequency, and an abnormally large peak in the response may be
`obtained.
`8.5. Closed-box Baffle. 1•2 The most commonly used type of loud(cid:173)
`speaker baffle is a closed box in one side of which the loudspeaker is
`mounted. In this type, discussed here in considerable detail, the back
`side of the loudspeaker is completely isolated from the front. Customary
`types of closed-box baffles are shown in Figs. 8.2 and 8.3. The sides are
`made as rigid as possible using some material like 5-ply plywood, 0.75 to
`1.0 in. thick and braced to prevent resonance. A slow air leak must be
`
`'D. J. Plach and P. B. Williams, Loudspeaker Enclosures, Audio Engineering, 36:
`12jJ. (July, 1951).
`
`L
`
`THX Ltd. Exhibit 2009 Page 7
`IPR2014-00235
`
`

`

`212
`
`LOUDSPEAKER ENCLOSURES
`
`{Chap. 8
`
`SUMMARY OF CLOSED-BOX BAFFLE DESIGN
`
`1. To <kkrmine the volume of tl1e closed boz:
`a. Find the values of fo (without baffie) and CMs from Par. 8.7 (pages 229 to 230).
`Approximate values may be determined from Fig. 8.5b and d.
`b. Determine So from Fig. 8.5a, and calculate CAs = CMsSo•.
`c. Decide what percentage shife upward in resonance frequency due to the
`addition of the box you will tolerate, and, from the lower curve of Fig. 8.11, deter(cid:173)
`mine the values of C.tsi CAs and, hence, Cu.
`
`d. Having C,.s, determine the volume of the box from Eq. (8.7).
`e. Shape and line the box according to Pars. 8.6 (page 227) and 8.5 (page 217).
`2. To determine the response of the loudspeaker at frequencies below the rim resonance
`frequency (about 500 cps):
`a. Find the values of MMn, RMs, C~o~s, Bl, Rs, and So from Par. 8.7 (pp. 228 to
`232). Approximate values may be obtained from Fig. 8.5, Table 8.1, and the sen(cid:173)
`tence preceding Table 8.1.
`C~o~sSo•, and RAs - RMs/So2•
`b. Determine llf AD "' J,J ~o~o/So•, CLs -
`c. Determine lll.tR, x,.R, .III,.,, CAB, and Mu from Eqs. (8.4) to (8.8).
`d. If the flow resistAnce and volume of the acoustical lining are known, deter(cid:173)
`mine RAs irom Fig. 8.8. Otherwise, neglect RAs to a first approximation.
`e. Determine the actual (not the rated) output resistance of the power amplifier,
`R.. All the constants for solving the circuit of Fig. 8.4 are now available.
`f. Calculate the total resistance RA, total mass MA, and total compliance CA
`from Eqs. (8.19) to (8.21). Determine w 0 and QT from Eqs. (8.22) and (8.23).
`g. Determine the reference sound pressure at distance r from the loudspeaker
`by Eq. (8.27).
`
`h. Determine the ratios of the driving frequencies at which the response is
`desired to the resonance frequency w0, that is, w/wo. Det~mine the ratio of
`RA/ M,t.
`
`i. Obtain the frequency response in decibels relative to the reference sound
`pressure directly from Figs. 8.12 and 8.13.
`
`provided in the box so that changes in atmospheric pressure do not dis(cid:173)
`place the neutral position of the diaphragm.
`Analogous Circuit. A closed box reacts on the back side of the loud(cid:173)
`speaker diaphragm. This reaction may be represented by an acoustic
`impedance which at low frequencies is a compliance operating to stiffen the
`motion of the diaphragm and to raise the resonance frequency. At high
`frequencies, the reaction of the box, if unlined, is that of a multiresonant
`circuit. This is equivalent to an impedance that varies cyclically with
`frequency from zero to infinity to zero to infinity, and so on. ~This vary(cid:173)
`ing impedance causes the frequency-response curve to have correspond(cid:173)
`ing peaks and dips.
`
`Part XIX]
`
`SIMPLE E~CLOSURES
`
`213
`If the box is lined with a sound-absorbing material, these resonances are
`damped and at high frequencies the rear side of the diaphragm is loadeti
`Vl'ith an impedance equal to that for the diaphragm in an infinite baffle
`radiating into free space.
`At low frequencies, where the diaphragm vibrates as one unit so that it
`can be treated as a rigid piston, a complete electro-mechano-acoustic~l
`circuit can be dra"wn that describes the behavior of the box-enclosed
`loudspeaker. This circuit is shown in Fig. 8.4 and was developed by
`procedures given in Part XVII.
`Some interesting facts about loudspeakers are apparent from this
`circuit. First, the electrical generator (power amplifier) resistance RQ
`Front side of
`diaphragm
`.
`radiation
`
`Electrical
`~~·~
`
`Mechanical part
`cifloUc!speat<er
`
`t
`c,.fl.l
`(B1 +R.e)SDI
`
`~~~~-o~~
`RAs u.
`
`XAB
`
`Fxo. 8.4. Circuit diagram for a direct-radiator loudspeaker mounted in a closed-box
`baffie. This circuit is valid for frequencies below about 400 cps. The volume velocity
`of the diaphragm = U,; e. = open-circuit ,·oltage of generator; R, = generator
`resistance; RIS =voice-coil resistance; B =air-gap flux density; t - length of wire
`on voice-coil winding; So =effective area of the diaphragm; MAD - acoustic mass
`of diaphragm and voice coil; CAs ~ tots! :1coustic compliance of the suspensions;
`R .. s - acoustic resistance in the suspensions; m.~R, XAR = aeoustic-radiation imped(cid:173)
`ance from the front side of the diaphragm; R,.s, X,u - acoustic-loading impedance of
`the box on the rear side of the diaphragm.
`and the voice-coil resistance RE appear in the denominator of one of the
`resistances shown. This means that if one desires a highly damped or
`an overdamped system, it is possible to achieve this by using a power
`amplifier with very low output impedance. Second, the circuit is of the
`simple resonant type so that we can solve for the voice-coil volume
`velocity (equal to the linear velocity times the effective area of the dia(cid:173)
`phragm) by the use of universal resonance curves. Our problem becomes,
`therefore, one of evaluating the circuit elements and then determining
`the performance by using standard theory for electrical series LR(' -::ircuits.
`VaLues of ELectrical-circuit Elements. All the elements shown in Fig.
`8.4 are in units that yield acoustic impedances in mks acoustic ohms
`(newton-seconds per meter5), which means that all elements are trans(cid:173)
`formed to the acoustical side of the circuit. This accounts for the effec(cid:173)
`tive area of the diaphragJ;ll So appearing in the electrical pn.rt of the
`circuit. The quantities shown are
`eQ = open-circuit voltage in volts of the audio amplifier driving the
`loudspeaker
`
`THX Ltd. Exhibit 2009 Page 8
`IPR2014-00235
`
`

`

`215
`-
`I
`1---
`
`-- -
`
`I
`
`{R
`I
`
`""
`-
`"J".-..
`-
`l 1 11--
`
`- \
`
`.., 180
`c=
`8
`5: 160
`~140
`"' ~ 0 120
`.: ,..
`~ 100
`~
`l! 80
`~ c
`r-
`~ 60
`g
`L
`"' a:: 404
`
` \
`
`
`
`1\
`\
`
`l
`16 18
`14
`.12
`10
`8
`6
`Advertised diameter in inches
`(b)
`
`SIM PLE ENCLOSURES
`
`Part XIX)
`
`50
`
`r--
`
`2a
`
`~ 40
`~ 30
`.§ c
`"' .~ 20
`~ 15
`E
`"' '5
`.~ 10
`t> 8
`ffi
`
`6
`52
`
`v
`
`/
`
`I'
`
`-
`
`/ v
`
`/
`/
`/ _L
`
`-
`
`15 20
`8 10
`4 5 6
`3
`Advertised diameter in inches
`(a)
`
`60
`40
`30
`20
`
`"' E
`~ 10
`.s 8
`~ 6
`"' :;; 4
`3
`2
`
`l
`I
`~ MMD and M/.tp
`
`/
`./
`
`V./
`~MD f-7'~rM~D
`L
`/ . /
`1'/
`."
`'L
`
`8
`6
`16
`14
`10
`16
`14
`12
`10
`8
`6
`12
`Advertised diameter .in inches
`Advertised diameter in inches
`(d)
`(c)
`FIG. 8.5a. Relation between effective diameter of a loudspeaker and its advertised
`diameter.
`FIG. 8.5b. Average resonance frequencies of direct-radiator loudspeakers when
`mounted in infinite baffles vs. the advertised diameters.
`FIG. 8.5c. Average mass of voice coils and diaphragms of loudspeakers as a function
`of advertised diameters. M.v:D is the mass of the diaphragm including the mass of the
`voice-coil wire, and M'uD is the mass of the diaphragm excluding the mass of the
`voice-coil wire.
`FIG. 8.5d. Average compliances of suspensions of loudspeakers as a function of adver(cid:173)
`tised diameters. Note, for example, that 3 on the ordinate means 3 X 10-• m/newton.
`not well behaved. That is to say, the resistances vary with frequency,
`and, when the wavelengths are short, so do the masses.
`The radiation impedance for the radiation from the front side of the
`diaphragm is simply a way of indicating schematically that the air has
`mass, that its inertia must be overcome by the movement of the dia(cid:173)
`phragm, and that it is able to accept power from the loudspeaker. The
`magnitude of the front-side radiation impedance depends on whether the
`box is very large so that it approaches being an infinite baflle or whether
`
`6
`
`a. s
`1\
`-~8
`8."
`~ .§ 4
`\
`~ ~ .. g~3
`0~
`
`;:a>
`a.E
`E c 8 ·- 2
`
`~
`
`"" !'....
`
`CMs
`
`-
`
`I
`
`-
`
`18
`
`18
`
`4
`
`v/'
`
`1
`4
`
`~ ...... , ..... _.
`
`214
`
`LOUDSPEAKER ENCLOSURES
`[Chap: 8
`B = flux density in the air gap in webers per square meter ( 1 weber I
`m 2 = 104 gauss)
`l = length of the wire wound on the voice coil in meters (1 m =
`39.37 in.)
`R. = output electrical impedance (assumed resistive) in ohms of the
`audio amplifier
`RB = electrical resistance of the wire on the voice coil in ohms
`a = effective radius in meters of the diaphragm
`SD = -rra2 = effective area in square meters of the diaphragm
`the
`Values of the Mechanical-circuit Elements. The elements for
`mec~anical part of the circuit differ here from those of Part XVII in that
`they are transformed over to the acoustical part of the circuit so that they
`yield acoustic impedances in mks acoustic ohms.
`lvf AD = M MD/SD2 = acoustic mass of the diaphragm and voice coil
`in kilograms per meter4
`MMD = mass of the diaphragm and voice coil in kilograms
`C.;.s = C,!sSD2 = acoustic compliance of the diaphragm suspen(cid:173)
`sions in meters5 per newton (1 newton = 105 dynes)
`C us = mechanical compliance in meters per newton
`RAs = RMs/SD2 = acoustic resistance of the suspensions in mks
`acoustic ohms
`RMs = mechanical resistance of the suspensions in mks mechanical
`ohms
`As we shall demonstrate in an example shortly, these quantities may
`readily be measured "1\'ith a simple setup in the· laboratory. It is helpful,
`however, to have typical values of loudspeaker constants available for
`rough computations, and these are shown in Fig. 8.5 and in Table
`8.1. The magnitude of the air-gap flux density B varies from 0.6 to
`1.4 webers/ m 2 depending on the cost and size of the loudspeaker.
`
`TABLE 8.1. T ypical Values of l, RE, and MAte for Various Advertised Diameters
`of Loudspeakers
`
`Advertised Nomina.l
`impedance,
`diam, in.
`ohms
`
`l,m
`
`RE,
`ohms
`
`jlf Me, mass of
`voice coil, g
`
`4-5
`6-8
`1Q-12
`12
`15-16
`
`3 .2
`3.2
`3 .2
`8.0
`16.0
`
`2.7
`3.4
`4.4
`8.0
`.. .
`
`3.0
`3.0
`3.0
`7.0
`...
`
`0.35- 0.4
`0.5 -o.7
`1.0 -1.5
`3
`12
`
`Values of Radiation (Front-S?.'de) Impedance. Acoustical elements. always
`give the newcomer to the field of acoustics some difficulty because they are
`
`1
`
`THX Ltd. Exhibit 2009 Page 9
`IPR2014-00235
`
`

`

`216
`
`LO UDSPEAKER ENCLOSURES
`
`!Chap. 8
`
`the box has dimensions of less than about 0.6 by 0.6 by 0.6 m (7.6 ft3), in
`which case the behavior is quite different.
`
`VERY-LARGE-SIZED BOX (APPROXIMATE INFINITE BAFFLE)
`mAR = radiation reSiStance for a piston in an infinite baffle in mks
`acoustic ohms. This resistance is determined from the ordinate
`of Fig. 5.3 multiplied by 407 I SD.
`If the frequency is low so
`that the effective circumference of the diaphragm (2-n-a) is less
`. than>-, that is, ka < 1 (where k = 2Tr/A) \Ra may be computed
`from
`
`Po = 0.0215j2
`O.l59w2
`m,u =
`c
`
`(8.2)
`
`X AR = radiation react ance for a piston in an infinite baffle. Determine
`from the ordinate of Fig. 5.3, multiplied by 407 / Sn. For
`ka < 1, X11R is given by
`X,..~~. = wM,u = 0.270wpo ..:.. 2.0f
`a -a
`
`(8.3a)
`
`and
`
`MAl = 0.270po -'- 0.318
`a
`- -a-
`
`(8.3b)
`
`MEDIUM-SIZED BOX (LESS THAN 8 FT3)
`\RAn = approximately the radiation impedance for a piston in the end
`of a long tube. This resistance is determined from the ordinate
`of Fig. 5.7 multiplied by 407 /Sn. If the frequency is low so
`that the effective circumference of the diaphragm (2-n-a) is less
`than A1 mAR may be COmputed from
`\R,L'! -= 1rj2po = 0.01076j2
`c
`
`(8.4)
`
`X AR = approximately the radiation reactance for a piston in the end of
`a long tube. Determine from the ordinate of Fig. 5. 7 multiplied
`by 407 /Sn. For lea < 1, XAR is given by
`
`X...n = wMAt ,., w(O.l952)po:: 1.45f
`a
`a
`
`(8.5a)
`
`and
`
`M.At = (0.1952)p0 _,_ 0.23
`
`a -a
`Closed-box (Rear-side) Impedance. The acoustic impedance Z;~e of a
`closed box in which the loudspeaker is mounted is a reactance X;~a in
`series with a resistance mAB· As we shall see below, neither XAD nor m..(B
`is well behaved for wavelengths shorter than 8 times the smallest dimen-
`
`(8.5b)
`
`217
`SIMPLE ENCLOSURES
`i>'art XIX]
`sion of the box. t If the dimension behind the loudspeaker is less than
`about >-/4, the reactance is negative. If that dimension is greater than
`A/4, the reactance is usually positive if there is absorbing material in the
`box so that the loading on the back side of the loudspeaker is approxi(cid:173)
`mately that for an infinite baffle.
`MEDIUM-SIZED BOX. For those frequencies where the wavelength of
`sound is greater than eight times the smallest dimension of the box
`(4L < >. for the box of Fig. 8.2), the mechanical reactance presented to
`the rear side of the loudspeaker is a series mas::; and compliance,
`
`1
`XAB = wMAB- wC;~s
`
`where
`
`CAB = Vps
`'Y 0
`is the acoustic compliance of the box in meters5 per newton and
`
`(8.6)
`
`(8.7)
`
`(8.8)
`
`MAs = Bpo
`?!'a
`is the acoustic mass in kilograms of the air load on the rear side of the dia(cid:173)
`phragm due to the box; and where
`V e ~ volume of box in cubic meters. The volume of the loudsp.eaker
`should be subtracted from the actual volume of the box in order
`to obtain this number. To a first approximation, the volume of
`the speaker in meters3 equals 0.4 X the fourth power of the ad(cid:173)
`vertised diameter in meters.
`'Y = 1.4 for air for adiabatic compressions.
`Po = atmospheric pressure in newtons per square meter (about 105 on
`normal days).
`1ra = ....;s;;; if the loudspeaker is not circular.
`B = a constant, given in Fig. 8.6, which is dependent upon the ratio
`of the effective area of the loudspeaker diaphragm Sn to the