US 1792655 A
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Feb. 17, 1931. E. 1 NORTON 1,792,555
` soUND REPRODUCER Filed May-.'51 1929 2 Sheets-Sheet l Arm/Wgr Feb. 17, 1931. E. 1 NORTON SOUND REPRODUCER nO rl 2 WT $5 E5.
VEN TOR E L. NoRro/v RAT/0 its length. The diaphragm 'Patented Feb. 11, 1931 UNITED v)STATES PATENT .o1-FICE Y EDWARDS L. NoE'ToN, or EAST ORANGE, LABORATORIES, rNcoRPoEATED, or 'Yoan v NEW JERSEY, AssIGNon To BELL Tumi:rrroNE NEW vom; N. Y., A CORPORATION or NEW.
SOUND REPRODUCER Applicationmed may a1, 1929. serial No. 367,487.A
nfor its prlncipal object the improvement of the response characteristics of devices ofl this type by the eliminationof variations due to the resonances of the vibrating system.
Another object is the elimination of mechanical reactance from the air column of the horn which constitutes the acoustic load upon the diaphragm, such reactance ordinarily entering into thezresonances ofthe system and contributing tothe unevenness of the response characteristic.
It has been` recognized thatl the vibratory system of `a sound reproducer, including the horn, constitutes a serially coupled chain of mass and elastic elements and may be regardedv as -a mechanical transmission line through which the vibrations ar'epropagated togaterminal load represented by the radiation resistanceof the'horn mouth. Y The horn itself constitutes a true wave transmission line in which th'emass and elastic properties are distributed in a continuous manner along and its driving mechanism, together with the air chamber customarily .f interposed between thev diaphragm and the horn, constitute a system iny` which the masses and the elasticities are subf, 'stantially segregated, or lumped, in separate elements and in which, therefore, a true space `wave does not exist. However, for a limitedy frequency range this lumped system can act in ama-nner analogous to a true transmission line and, by the proper ing of the elements, it can be ma e to transmit freely all vibrations in the range of frequencies' needed `for-the accuratereproduction of speech or music.
'Ifhe proportions heretofore used for the vibrating' elements t secure free transmission in a single`ibroad band covering the es- -sential speech range of frequencies, are such that the vibrating system is, in eifect, a chain *of uniform mass elements coupled serially by springs of uniform elasticity, the values of the masses and the elasticitiesbeing determined by the range of frequencies to be '.stantiall-y in accor whereby the effects of resonance are Joom-l eut oef-v` ,the invention in its'bestmanner it is esirlble. that the vibratory elementsshould' closelyroportiontransmitted and the impedance of the acoustic load. In such a system the resonances of the vibratory elements are substantially damped by the `acoustic load but'arenot so 'completely damped that the accentuation of the tones corresponding to the resonance frequenciesl is der lying tems of this type are clearly eX laine`d ini U. S. Patent 1,730,425, issued tober 8, 1929 to H. C. Harrison.. Y
eliminated. The principles unthe design and operation d.of'sys.
n In accordance with the presentinvention.
the masses of the elements of the coupled system are given progressively increasing values and the elastlcities are given progressively decreasing values from one section to another, the mass increments andthe dimnf dance withraldeinitelaw, pletely suppressed. For 'the ishing values ofthe elasticities being" suli' approximate simple masses andfsimplealllsticities at all vfrequenciesin thepspeech range and that the hornyshould have'a resistive impedance as free as possible frolnreactanca A feature of the invention directedto this-4 end is a modified form of the air clamber in front. of the diaphragm.A The (pening into the horn throat is in the form o an annulus the diameter of which bears aparticular ratio to the diaphragm diameter whereby the mass effect of the air in the chamber is annuled and `the chamber. is made to actas a pure elastic#A y ity. Another feature of the invention 1s a horn of novel form having the property that its impedance is completely free from reactanceat all yfrequencies in its useful range.
The cross sectionalarea of the sound passage varies in accordance` with two exponential functions of the length, one of the functions having increasing values and the other diminishing. In general it .resembles the logarithmic horn, but dili'ers therefrom in that the throat portion is longer and less tapered.
'In the usual constructions the dtphragm does not correspond to a pure mass, but rather to a simple mass in combination with an elastic restraint due to the edge support. This elastic restraint is also an undesired reactance which tends to produce irregularities in the response characteristic and al further feature of the invention relates to the elimination of these irregularities by the-adop-- trating'a theorem used in explaining the in vention;
Fig. 7 shows the type of response characteristic of the systems of the invention;
Fig. 8 is a schematic figure relating to the feature of the air chamber design;
Fig. 9 is a set of curves used in the determination of sions;
Fig. 10 shows the form of the acoustical horn of the invention; and
Fig. 1I shows by means of curves the impedance characteristic of the horn of Fig. 9.
The schematic diagram of Fig. l, repref seiiting the impedance relations of the sound reproducers of the invention 1s drawn in accordance with electrical conventions, but by the well known analogy between mechanical and electrical systems, it equally well represents the impedance'relations of a mechanical system. The system illustrated. 1s 1n the nature of a wave transmission line comprising in combination with an energy dissipative load resistance R, two line elements of impedances A4XR and AZXR, and three cupling elements R l, and p A5X A3X l AIX The terms line and coupling correspond respectively to the electrical terms series and shunt and serve to distinguish the functions of the different elements. An oscillatory lmotion is modified in velocity as it traverses a coupling element and in force as it traverses a line element. A'coupling element transmits. the forceimpressed on" it undiminished to the next line element and a line element transmits the velocity of the motion without change. lTheltransmission line to whichthe vibrating system of a sound v reproducer corresponds is generally of a very simple type, comprising line elements in the form of simple masses, and coupling elements in the form of springs. The energy dissipative load is provided by the air in front of the air chamber opening dimen the sound radiating device, or, if radiator is a horn, by the air column 1n the horn iu combination with the radiation from the mouth.
The analysis of the motion in a system of this sort is greatly facilitated by the concept of mechanical impedance.' This quantity provides a direct measure of the forced oscillatory veloci ty in a body or system in response to an oscillatory force applied thereto. It is defined as the ratio of the applied force, assumed to have a steady effective value, to the velocity of the body or of the system at the point of application. It is a vector quantity defining both the magnitude of the velocity and its phase diiference from the applied force. The impedance of a simple mass element is directly proportional to frequency, the velocity lagging 90 degrees behind the applied force. Expressed mathematically the impedance is equal to jmM, where e isQnr times ythe frequency, vM the mass, and the cus-sL mary operator 1/-1. The impedance of a massless spring measures the extension velocity, that is, the velocity of the one end` relatively tothe other, in response to an applied force. Its value is jg where S is the elasticity of the spring, and where the negative operator indicates that the velocity leads the applied force by 90 degrees. Following the established practice in electricaltheory the real component of the vector quantity denoting the impedance is termed resistance and the imaginary component istermed reactance. The impedances ofcomplex coupled systems can be expressed in terms of the impedances of elements by the same rules as apply to electrical systems. For example, a mass element supported byy a spring from a rigid abutment is a series combination, the impedanceof which is obtained by adding the component impedances, while a free mass to which the force is .appliedA the sound through a spring is a parallel combination.
In the system of Fig. 1 the 'line and the coupling impedances are pure mechanical reactances, i. e. combinations of masses and elasticities in which there is no energy dissipation. The impedance values are made up of three factors, -a common factor X which is an imaginary numerical quantity and which expresses the frequency variation of the impedance. a common factor R equal to the resistive impedance ofthe dissipative load,
and numerical coefficients l, a2, etc. givv ing the relative magnitudes ofthe impedances. Itis to be noted that the impedances of the line and the coupling elements are inversely relatedwith respect to their fre.-
.quency variations; thus the line elements may be simple masses having impedances proportional to frequency andthe coupling elements may be simple lelasticities the imenergy absorbed by the load resistance R is proportional to the square of the velocity therein and, therefore, to the square of the response at any particular frequency. In accordance With the invention the impedances are given` such relative values that the response of the system for a constant oscillatoryinput is propqrt'ional to the quantity l VW (l) l where n is the total number ofthe line and coupling impedances. This result is obtained by giving the coefiicients a1, a2 etc. the values sin When n is equal'to 5, as in Fig. 1, thenumerical values arev for the response characteristic gives theratio' i of the outputvelocity to the input velocity,
that is it shows the 'variation of the output velocity With frequency for a constant inputvelocity. A v
The mathematical steps in the determination of the coeiiicient values are discussed at length in. my copending application Serial No. 355,607, filed April 16, 1'929, and need not be reproduced here.
. The application of the foregoing principle to a -sound reproducer Will be described in connection with the device illustrated in Fig. 2. This figure shows in section a stylus driven phonograph reproducer the elements of the vibrating system of which comprise a diaphragm 10, clamped at its edge Within a casing 11, an air chamber 12, formed between p Aconventions of Fig. 1
thediaphra m and the front face of the casing, a sty us arm 13 pivoted at 18 on they casing, and a stylus v14. When used for reproduction from a phonograph record, the stylus velocity is determined only by .the speed of the record and the amplitude of the groove. and the accuracy of reproduction depends upon the uniformity with which this velocity is transferred to the air in the horn. The response characteristic therefore corresponds to the frequency variation of the ratio of the output to the input velocity. The air chamber 12 opens into a horn 15 'Which constitutes the terminal acoustic load.
In the particular device illustrated the air chamber communicates with the horn by an annular opening 16l around the base of a solid conical block 17 which is mountedin an expanded portion of the horn throat. The features of the` horn design and of the throat openingby Which a truly resistive and constant load impedance is obtained Willbe discussed later.
The schematic arrangement of the vibrating system is shown in Fig. 3 in which the are employed to disish the line and t'fie coupling elements in which also the electrical symbols for tin inductance and capacity are used to indicate the corresponding quantities of mass and elasticity respectively. It should be remembered, however, that although the impedances of a capacity and of an elasticity vary in the same Way with frequency, their magnitudes are inversely related, thecorrespondence bing between elasticity and the reciprocal of capacity.
- The resistance R represents the Aterminal load constituted by the impedance of the horn. The impedance of the air chamber is represented by-a simple elasticity S1 in shunt to the load. Ordinarily the air chamber, due to the effect ofthe air mass, does not act like a simple elasticity except at lo-W frequencies, but it has been found that, by using an annular opening of vproportions to be described later, the mass effect can be eliminated and the air made to act as a pure elasticity. The diaphragm is represented by a mass M2 in series with an elasticity S2, the elasticity being due to the edge support o'f the vdiaphragm. By forming the diaphragm of thin sheet metal and embossing it in a suitable manner to make the center portion rigid, it may be made to approximate closely to a simple mass, the edge elasticity being sol small that its effect, to a first approximation,
is the effective ity S is that of the stylus likewise trans- .ferred to the axis of the diaphragm, the
value b'eing transformed in accordance with a transformation i'atio introduced by the lever action of the stylus arm. The stylus and stylus arm elasticities may be taken as the ratio of force to linear deiection at the 'stylus point and yat the end of the stylus arm respectively when the arm is rigidly clamped at the pivot.
If the edge elasticity S2 of the diaphragm be ignored, as it may be in the vcase of an ideal piston diaphragm, the system then includes only simple masses as line elements and simple elasticities as coupling elements,
the former having impedaiices proportional to frequency and the latter having iinpedances inversely proportional to frequency.
The values of the masses and the elasticities where fo is the frequency at which X is numerically equal to unity. vThe response is then proportional to the quantity.
lf'; f ver the index 10 appearing since there are in all five impedance elements. With a constant resistive horn impedance, the sound energy delivered to and radiated by the horn is proportional to the square of the above quantity when the input velocity is constant.
comes veryV small while for lower frequencies it is substantially equal to unity. The fiequency fo is therefore an important design parameter since it marks the limit of uniform response. Comparingthe impedances of the corresponding elements of the systems'of Figs. 1 and 3, the values of the masses andthe elasticities required to give the desired response characteristics are readily obtained. These values are as follows:
At fre uencies creat-er than the res onse beq h fo p f velocity, `although it may increase the input -The values ofthe masses and the elasticities are thus fully determined when the horn impedance is known and the limiting frequency of uniform response has been as signed.
The .forni of the response characteristic is illustrated in Fig. 7 in which the magnitude of the ratio of the input to the output velocity is plotted against the ratio fo The full line 20 shows the response of a tive element system in accordance with the invention. For comparison purposes the dotted line 21 shows the response of a similar system having uniform line masses and uniform coupling elasticities. Both curves are drawn on the assumption that the elements are quite free from energy dissipation, the eii'cct of which is to add a slight downward slope with frequency to the full line curve and to diminish considerably the high peak in the dotted curve. The characteristic diii'ercnce between tlie two types of response is not changed. l
The foregoing formulae are developed on the assumption that the edge elasticity of the diaphragm is negligibly small, but in most practical cases it is desirable that this quantity should be taken into account in proportioning the system. By means of a theorem of equivalence which is illustrated in Figs. 5 and 6 it can be shown that the systemof Fig. 3, including the elasticity S2, is equivalent to a simpler related system involving only simple line masses and simple coupling elasticities to which is connected in series at the input end an elasticity proportional to S2 but of a modified value. The presence of this series elasticity does not modify the input impedance of the system and, especially at low frequencies. cause the stylus point to react more strongly against the sides of the record groove. The simplified s vstem'may be proportioned in the manner indicated above and the necessary modifications may be made in the actual system in accordancewith the relationships establishing the equivalence.
Fig. 5 shows a combination of'two similar impedaiices of values Z and pZ,'one in shunt and theother in series, the series impedance,
being to the right of the shunt impedance' Regarding this as a portion of a transmission line, the combination may be replaced by that shown in Fig.'6 which comprises a series impedance f 1 27 to the right of which is a shuntimpedance earlier By this equivalence the relative positions of the series and the` shunt impedances are` changed and their values modified by constant numerical facto-rs'.` The theorem may be applied to the system of Fig. 3, first to the combination S2, S3 and'then again to the combination of S5 and the elasticity. appearing M4 as the result of the first application. The ideal transformers may of course be movedto any point inthe system without affecting the-equivalence provided appropriate changes in the impedance values are made.
As the result of the steps outlined above the system of Fig. 4 is obtained which is the `precise equivalent of that of Fig. 3 in respect of its transmission properties. has changed the elasticity S3 3(1-l-p), or S34-S2. introduced a new transformation` ratio of 1: (1+g)2, where that is, g is equal to the ratio" of the modified elasticity appearing in series with M4), after the first step to kthe shunt elasticity S5. The two'transformations are represented' in the figure'by a single transformer having a ratio equal to their product.
The portion of Fig. 4to the right of the transformer may be computed rigidly in accordance' withfthe method described in the paragraphs to obtain the response 'to4 the value a characteristic defined by Formulae 1 and 3 and theimpedance coefcients of cal system readily follow. I
The designof an actual sound reproducer of thetype shown-inFigQ will now be described. The most convenient starting point is the assignment ofv the frequency rangegof uniform response and the selection of a diaphragm of practical dimensions from a man-v ufacturing standpoint. Let it be-assumed is 4000 c. p. s. a diameterof 4.5 cms. and a mass of 0.20 grams. Such a diaphragm may be constructed from alumi- 'num or; aluminum alloy sheet about .0035 em.
. thick, the central portion being embossed in conical or other form to ive rigidity. The
edge stiffness S2 may be ta en asv5 10'3 c. g. s.
for a diaphragm of these dimensions. The effective impedance that vthe horn l should have is found from the relationship the coefficient a2 having the value 0.896 corrlhe first stepl The second step has 'l ured at the throat of a horn in the actual physislsarfa '(7) a1 whichl gives a numerical value of 455 106 70 g. s; For the stylus 4arm elasticity we have from which S3=97 106 c. g. s. v The stylus arm effective mass is given by stylus is given by and 85:77.? 106 c. g. s. The dyiiamicalTL proportions of the yelements having been found vthe geometrical forms and dimensions can be arrived at by known methods. The required born impedance has been found to be 5600 c. g. s. Y This is the value effectiveat the diaphragm and is different from the value measured `at the throat aperture due to the impedance transforming. effect of the air chamber. The value of the impedance'measgeneral is not constant `,with frequency and is not a pure resistance,
sistive within the working range and is substantially constant. This constant value is equal to 41A1 c. g. s., Where A1 is the throat area. Taking account of the transformation ratio due to the air chamber, as described in the hereinbefore mentioned Patent 1,730,425 to H. C. Harrison, the effective im-l` pedance at the diaphragm is given by where A2 is the area of the diaphragm. From this equation, knowing R and A2 the required value of A1 is found to be 1.85 square centimeters. The air' chamber elasticity ,S1 is determined by its volume and its diameter in accordance Withthe formula Where V is the volume. The volume necessary to make S1 have the required value of but with the type of horn to be described later the impedance is 'purely reloo 455 l0l c. s. is found from this equation to be 0.785 c. c., which with a diameter of 4.5 cm. corresponds to a depthof .05 cm.
The proportioning of the stylus arm to have the required effective mass and 'elasticity is a matter of mechanical design and may be carried out by Well known processes. The
phragm. If a more flexible needle is used' the length from the needle point to the pivot should be diminished to provide the proper transformation.
In the foregoing, it is assumed that the air in the air chamber acts as a simple elasticity, but with the ordinary construction in which the horn is coupled to a central aperture this Will not be the case. Due to the uniform distribution of mass and elasticity throughout vthe air volume the motionin the air .chamber is a true Wave motion in which the Wave is propagated parallel to the surface of the diaphragm towards the aperture. At loW frequencies the Wave is so long in comparison with the longest path in the chamber that the space variation of the motion is unimportant, but at high frequencies the Wave length becomes short enough so that a considerable fraction" of the iva-ve may be encompassed Within the dimensions of the chamber and a nodal point may exist at the horn aperture. Under such conditions it is possible to have the response fall to zero at some frequency Well Within the range necessary for good re production of speech or music. The distributed constant7 or mass effect of the air, to Which this action is due, can be substantially eliminated by the use of an annular opening of a properly chosen mean diameter. If the mean diameter of the annulus were equal to the diaphragm diameter, that is, if the sound lwere taken off from the outer edge of the diaphragmthe conditions would be just as bad as in the case of a center opening. At
some intermediate value it would be expected that the conditions would be most advanta geous and the frequency at which the response fails Would be moved to the highest value. It has been found and can be shown mathematically that the optimum value` of the mean diameter of the annulus is equal to 0.63 times the diameterof the diaphragm; With this proportion the mass effect of the air is so vcompletely eliminated that it is negligible at all frequencies required for the highest quality of reproduction.
The determination of the proper radii for the annulus opening is illustrated by Figs.
8 and 9. In Fig. 8 ro represents the diaphragm radius, r1 the inner radius of the opening, and r2 the outer radius. .In Fig.9 the values of the ratios y l 7' -1 and -2 To To are plotted-as ordinates against the values4 of the ratio ,A2, A1 being the aperture area and A2 the diaphragm area as before. The ratio measures, as alreadypointed out, the impedance transformation inthe air chamber and determines the eective value of the load impedance. These curves represent the solution of the equation Where J1 indicates a Bessel function of the kfirst order.. The principles underlying the analysis from Which the above equation is found areas follows: The annular openingl from the air chamber is used for the purpose of insuring that the Wave transmission paths `mum length is not sufficient for the best rcsults. For example, 1n the case of a uniform.
air chamber with the opening at half the radius the volume of air displaced in the region outside the annulus Would be three. times as great as that displaced in the region inside and although the Wave paths may be o'f equal length the disparity of the air volumes would givey rise to interference effects in the neighborhood of the annulus. It is thus to be cxpected that the optimum radius would be somewhat greater than half the radius of .the chamber. p
To obtain the best value of the annulusV .diameter the dierential equation for the Sound Waves in the chamber may be expressed in polar coordinates to suit the circula-r configuration. ,The solution is then obtained in terms of Bessel functions, und after putting in the boundary conditions of the problem it is found that the solution indicates a series of resonances at various frequencies at Which substantially no.power is delivered to thel horn. Since it is desired toftransmit a bandv of. frequencies from some very low value up to as high a frequency as possible it is most important to suppress those resonances which occur at the lower'frequencies. Each ofthe resonant terms in the mathematical solution has a coefficient the magnitude of which may be changed by changing the radius of the annular opening. By placing the openingnat the particular point defined by Equation (12) the coefficient of the lowest frequency resonance is made equal to zero, or in other words,
`the lowest frequency resonance no longer occurs. For chambers of the ordinary size used in loud speakers lor phonographs the second resonance occurs at a very high frequency outsideof the ordinary speech range and the result is that by the elimination of the first resonance substantially uniform efficiency is` maintained over the whole speech range.
The dotted curve of Fig. 9 represents the Where rx denotes the radius at a distance X along the axis from the throat, n denotes the radius at the throat, and b is a coei'cient del ning the rate of expansion. The above equation may also be written in the form .i which shows that the radius varies in accordance With two exponential functions, one of which increases with andthe other of which diminishes.` Both are equally important at the small end ofj the horn but at the large end the increasing termis most important. In Fig. 10 the dotted outlinrepresents a simple exponential horn of the same expansion coefficient, only the throat portion being indicat ed, since the two outlines are indistinv guishable at the large end. The figure indiythroat. horn is shown by the curves of Fi 11 in exponential horn.
Cates that the horn of the invention' is somewhat longer than thev corresponding expon` ental horn and tapers more gradually at the Theimpedance characteristic of the which `the ratio of the impedanceto the final steadyvalue R is plotted against frequency. Curves 21 and 22, plotted to loga-` rithmic scales, correspond to the horn of the invention and curves 23 and 24 to the simple The solid lines represent resistance values and the dotted ,lines-reactfrequency" and impedance" 'the frequency increase progressively in the direction away a'nces. Logarithmic scales are used for both v alu'es being given in terms of the ratio i A. i fc where fc is thecutfoi" frequency f the horn.
At this frequency, which is given by a fsa?.
'coefficient has the same cut-oil' frequency but Vat the higher frequencies, that is in its working range, it is not free from/reactance. In
. systems of the type described the. presence of reactance in the load impedance is prejudicial to the realization Vof the desired response characteristic,l but by the use of the special horn contour this is eliminated and the improved response is obtained. I
The horn need not be constructed with a straight axis and with a-circular section as shown in the figure, but may be formed in accordance with the common practice of folding to diminish the space required and the cross section may be of any shape so long as the area varies in the manner ,defined byEquations 13 and 14.
While the invention has been described .with'particular reference to a stylus driven phonograph reproducer its application is not limited thereto, but may include acoustic recording devices and also electrical telephone receiversand transmitters, for example of the type shown in my earlier U. S. Patent N o. 1,681,554, issued August 21, 1928. In the latf' ter the vibrating system is driven by a force applied to a magnetic armature, which con-V stitutes aline mass, and is transmitted to the diaphragm through one or more intermediate elements. If the elements are proportioned in the manner described above the system will have the property thatptheoutput velocity in response. to a constantforce input varies with frequency in the manner that is characteristic of the invention. i What is claimed is :Iv v
. l. A sound reproducer comprising a diaphragm, a horn, an air chamberbetween said (diaphragm and said horn, and means for vibrating said diaphragm in accordance withy sound vibrations, said diaphragm, air chamber, and vibrating means constltutmg a serially coupled system of masses and elastici- .ties in which the effective values lof/the masses from the horn and the effective values Aof the elasticities diminish substantially as described whereby the sound energy delivered to the horn for a constant input is substantially proportional to where f is the Vibrationv frequency, fo a preassigned frequency deining the upper limit of uniform response, and n is the number ofI" elements in the coupled system.
A sound reproducer in accordance with claim 1 in which the effective values of the masses and of the reciprocalsof the elasticities vary progressively in the directionaw'ay from the horn in proportion to the the coefiicients l Where the subscripts 1, 2, 7, n, denote the order of the elements of the Vibrating system counting from the horn.
3. A sound reproducer in accordance With claim 1 in which the air chamber is coupled Ato the horn by an annular passage the mean diameter of the annulus being substantially 0.63 of the free'diameter of the diaphragm whereby the mass effect of the air in the air chamber is substantially eliminated.
4. In a sound reproducer a' diaphragm, an air chamber enclosing said diaphragm and a horn the small end'of Which opens into said air chamber, the opening from said horn into said air chamber being in the form of an annulushaving a mean diameter substantially equal to of the free diameter of said diaphragm.'
5.. A sound reproducer in accordance `With claim 1 characterized in this that the cross sectional area of the horn increases progressively With the distance along the axis from the small end in accordance with the formula Where A0 is the throat area, and A is the area the formula A=A0 coshI 2a;
Where A is the area at the distance w from the small end and A0 is the area of the small end opening.
In witness whereof, I hereunto subscribe by name this 27th day of May, 1929.
EDWARD L. NORTON.