US 2396222 A Abstract available in Claims available in Description (OCR text may contain errors) March 5, 1946. FQLDY SOUND RECEIVING SYSTEM Filed Oct. 26. 1942 4 Sheets-Sheet l sE/vs/r/v/Ty, K (:05 6 I l I' I 2 I l i x----------' -----------x E I I I i l I SENSITIVITY, K C052 6 INVENTOR. FOL D Y LESLIE L. March 5, 1946. FOLDY SOUND RECEIVING SYSTEM Filed Oct. 26, 1942 4 Sheets-Sheet 2 SENSITIVITY, K 0059 INVENTOR. [[SL/E L, FOLDY March 5, 1946. LL, FOLDY 2,396,222 SOUND RECEIVING SYSTEM Filed Oct. 26, 1942 4 Sheets-Sheet 3 SENSITIVITY, K 0056 OUTPUT OUTPUT INPUT ATTEN. OUTPUT OUTPUT 1N VENTOR. LESLIE L. FOLDY Patented Mar. 5, 1946' 7 sounn rmcsrvme srs'rmu Leslie L. Foldy, New York, N. Y., asslgnor to The Brush Development Company, Cleveland, Ohio, a corporation of Ohio ApplicationOctober 26, 1942, Serial No. 463,328 23 Claims. ing of remote airplanes. submarines and the like, it is desirable that a sound pickup device or system shall have pronounced directional characteristics. A certain amount of directivity may be obtained, of course, by employing one or more large directional horns, or the microphone may be placed at the focus of a parabolic reflector or disposed in a recess in the surface of a large baffle. Horns and baflles are unwieldy, however, and it has also been observed, when employing a microphone or a microphone-array, the eifective size of which is large in comparison with the wave-length of the sound that it is desired to receive, that it is somewhat difiicult to obtain exact bearings because of the presence of side lobes in the response characteristics. The lobes tend to cause confusion, inasmuch as sometimes they are rather numerous and large and are disposed in angular relation to the axis of maximum sensitivity. Another disadvantage resulting from th presence of lobes is that the microphone, onmicrophone-array is sensitive to extraneous sounds coming from sources along the axes of the lobes, thus decreasing the signal-to-noise ratio of the system. It is, accordingly, an object of this invention to provide a sound receiving system having a response-characteristic that is substantially free from lobes. Another object is to provide a system of the type described that shall be more highly directional than analogous systems heretofore known. Another object is to provide a system of the type described wherein commercially available microphones may be employed without substantial structural or electrical modification thereof. Another object is to provide a system of the type described the directional response charac teristics of which shall be substantially independent of the frequency of the sound waves incident thereon. Another object is to provide a sound receiving system the response characteristic of which may be varied. A further disadvantage of many directional sound receiving systems is the rather wide angle, with respect to the axis of maximum sensitivity, over which the response does not perceptibly vary. To sharpen the response, it has been proposed to employ an amplifier having a non-linear characteristic such, for example, as the amplifier disclosed in the United States patent to Hammond, No. 2,262,457. Non-linear amplifiers greatly improve directional reception if the frequency of the sound from the source is reasonably constant, but the distortion caused thereby renders them impracticable if voice or musical sounds are to be received and observed or recorded for later observation. Another object of th invention, therefore, is to provide a directional sound receiving system that shall not require the utilization of especially designed non-linear electrical amplifiers and, ac-. cordingly, a system that may be employed for the reception of sounds having a wide range of frequencies. An additional object is to provide a sound receving system of the type described, the directional properties of which shall not depend critically upon the exact location of the various components thereof. The cornerstone, so to speak, of a directional sound receiving system embodying the invention is a bi-directional transducer having a response characteristic of the "cosine" type. Such transducer may be a singl microphone of the so-called ribbon type, but for purposes of explanation it is convenient to consider it as being constituted'by two microphone-units having the same sensitivity, each being of the non-directional pressureactuated type, displaced apart a distance "d along an axis Y-Y of maximum sensitivity, the distance being of the order of or less than one fourth of the wavelength of sound at the highest frequency at which it is desired to have directional reception. With respect to an output circuit, the two microphone-units are so connected in opposing relation, that the output of the system is zero in response to plane waves coming from directions normal to the YY axis, while the response to sound from other directions is proportional to Kn cos 0. Through research verified by mathematical analysis, it has been determined that if two transducers, each constituted by a pair of microphoneunits, as described above, are so aligned that the distance between the terminal units is of the order of 2d, the intermediate units sharing substantially the same space and the connections of the second transducer to the output circuit being reversed with respect to those of the first transducer, the response characteristic of the composite system is proportional to Kb cos 0. Instead of utilizing two discret intermediate units, the pair may be replaced by a, single unit havin twice the sensitivity of a terminal unit, without altering the response characteristic of the array. If two microphone-arrays, of the type just detance between the terminal units is of the order of 3d, the connections of the second array being reversed, with respect to the output circuit as dey scribed, each having a response proportional to J Kb cos 0, are so aligned and spaced that the disscribed, the response of the new system is proportional to Kc cos 0. This system will comprise two spaced apart intermediate microphone units, each having three times the sensitivity of a ter- I necessary, provided, of course that microphone units having the correct sensitivity are available and that phase-shift, within the system, is prevented. The response characteristic of a system comprising M units in line, each having proper connections of its terminals and proper sensitivity, may be said, in general, to be proportional to Ke cos-- and, as will be explained hereinafter, the sensitivity of the intermediate units, with respect to the terminal units, may be calculated in advance for an array intended to have a predetermined response characteristic. As will also be shown hereinafter, the factor "K depends upon the response-pattern. of the array as determined by the number and sensitivity of the microphone units or transducers employed. The novel features considered characteristic of the invention are set forth with particularity in the appended claims. The invention itself, however, both as to its organization and its method of operation, together with additional objects and advantages thereof, will be understood best from the following description of certain specific embodiments thereof, when read in connection with the accompanying drawings, in which: Figure 1 is a diagrammatic view illustrating a "cornerstone transducer having a directional response characteristic proportional to Ker cos 0; Figure 2 is a polar diagram illustrating the directional response characteristic of the transducer shown in Figure 1; Figure 3 is a diagrammatic view illustrating a microphone-array havinga directional response characteristic proportional to Kb cos 0; Figure 4 is a polar diagram illustrating the directional response characteristic of the microphone array illustrated by Figure 3; Figure 5 is a diagrammatic representation of the system exemplified by Figure 3, to which reference will be made in the mathematical analysis of the response characteristic thereof; Figure 6 is a diagrammatic view illustrating a microphone array having a directional response characteristic proportional to Kc cos 0; Figure 7 is a diagrammatic representation of the system exemplified by Figure 6, to which reference will be made in the mathematical analysis of the directional response characteristic thereof; Figure 8 is adiagrammatic view illustrating a microphone array having a directional response characteristic proportional to Kd cos 0; Figures 9 and 10 are diagrammatic views illustrating alternative means whereby the directional response of -a microphone array may be controlled; and Figure 11 is a table giving the number of microphone units, the sensitivities and phasing thereof, as well as the directional characteristic, for a few simple microphone arrays constructed and arranged according to this invention. In all figures of the drawings, equivalent elements are similarly designated, and in Figures 1, 3, 6, 8, 9 and 10, each microphone-unit is illustrated as having a black terminal designated plus and a white terminal designated minus, for the purpose of indicating the polarity of the potential developed thereby in response to sound pressure greater than atmospheric, the polarities being reversed for rarefaction. Referring now to Figure l of the drawings, the "cornerstone" of a microphone array constructed according to this invention may be considered as constituted by a pressure-gradient transducer comprising two. non-directional pressure type microphone-units, A and B, spaced apart a distance d along an axis of maximum sensitivity, Y-Y, and connected in opposing relation with respect to an output circuit. Such being the case, the system illustrated by Figure 1 has minimum sensitivity to sound'arriving from directions substantially normal to the axis Y-Y, the response being maximum along the said axis. If the distance d,between the microphone-units, is defined by the expression i being the wavelength of sound at the highest frequency to be received, the directional response of the system is proportional to Ka cos 0, represented graphically by the well-known polar diagram shown in Figure 2. For optimum results, as will appear hereinafter, (1 should be less than To obtain the next higher order of directivity, defined by the expression Kb cos 0, the microphone array illustrated by Figure 1 is supplemented by another array having the same directional characteristic. The new array, illustrated by Figure 3 of the drawings, includes twotransducers, each comprising a. pair of equally sensitive non-directional microphones A and B, that are so aligned that their axes of maximum sensitivity coincide or approach closely to coincidence, and the terminal units of the array are displaced apart along the axis by a distance of the order of 2d as hereinabove defined. The connections of the second transducer are the reverse of those of the first, with respect to the output circuit, as illustrated. Also, for the purpose of mathematical analysis, it is to be assumed that the two equally sensitive intermediate microphones B, A, are so close to each other that they may be replaced by a single microphone having twice the sensitivity of one of them. This is not necessary for proper operation of the device in the manner indicated, however For the mathematical proof of the foregoing statement with respect to the directional response characteristic of an array exemplified by Figure 3 of the drawings, attention should be directed to Figure 5 which shows three non-directional microphone units disposed along an axis YY- aaeaaea and each having a sensitivity A. The negative signs in the drawings indicate that the response of the terminal units is 180 out of phase with the response of the intermediate unit, insofar as the output is concerned. The circuit connections have been omitted, in order to simplify the drawings; they correspond to those shown in Figure 3. The symbol denotes the angle of incidence of the sound wave, measured away from the axis of maximum sensitivity, Y-Y. . If the response of microphone element 2 to a sound wave having a frequency J, a wavelength A, and a velocity u is Is -2A cos 2m then, since the wave will reach element l at a time d cos 0/v=d cos 9/1) earlier, the response of microphone element i will be and similarly the response of element 3 which the wave will reach later by the same time interval will be =A cos (21rft-21rd cos e/i) =2A cos 2wft-A cos 27rfi cos (21rd cos H/A) A sin 21rft sin (21rd cos (ilk)- Al cos 21rft cos (21rd cos HIM- A sin 21rfi sin (21rd cos 6/)\) =2A cos 2wrft (l-cos (21rd cos 0/)0) If d/ then to Within (21rd cos (ilk) cos (21rd cos 0M) =1 2 so that I=A (ac d cos 6M cos 21rft The directional response of the system, accordingly, will be of the type defined by the expression: which corresponds in form to the expression Kb cos 6 as given in connection with the discussion of Figure 3 of the drawings. If d )vi, the response will differ from Kb cos 9, but will still have increased directionality over a single cosine type transducer. If the microphone array exemplified by Figures 3 and 5 of the drawings, having a directional response characteristic proportional to Kb cos 0, is supplemented by a similar array having the same overall response characteristic, the microphone units being so aligned along the axis Y-Y of maximum sensitivity that the distance between the terminal units is of the order of 3d, the connections of the second array being reversed with respect to the output terminals, the system will have a response, or sensitivity, proportional to Kc cos- 0. Such a system is exemplified by F ure 6 of the drawings, and it is to be understood that the intermediate groups, each constituted by two non-directional microphones, (B+A, A) and (B, B-l-A), may be replaced, respectively, by single microphones having three times the sensitivity of either of the terminal microphone units. In Figure 8, the substituted microphones, are designated (B+A+A) and (B+B+A). It is realized that the system adopted for designating the various transducer units may be somewhat confusing to the reader. It is believed, however, that the system more clearly exemplifies the replacing of several microphones by a single unit, of sensitivity greater than A," than if consecutive numerals were employed. For the mathematical proof of the foregoing statement, attention may now be directed to Fi ure '7 of the drawings which exemplifies an array of aligned microphone units spaced apart a distance "d" along an axis Y- Y of maximum sensitivity, the total distance between the terminal units being of the order of 3d. With respect to a wave approaching at an angle 0 away from the axis Y-Y, the response of the first complex element will be: I1==(B cos 0) cos 21rft The response of the second will again lag in time by d cos 6/1: so that its response will be I2=(B cos 0) cos 21d (td cos mm) The combined response will then be I=I '+I;=B cos 0 cos 21rft B cos 6 cos (21rft21rd cos B/A) =B cos 0 cos 21rft B cos 0 cos 21rft cos (27rd cos 6/)\) B cos 6 sin 21rfi sin (21rd cos B/A) 8 cos 9 [(1 -cos (21rd cos 0/)\)) cos 21ft- (sin (21rd cos 0/)\)) sin 21rft =PB cos 6 cos (21rft+) m where and d [1cos (21rd cost/ If d/A then,.to within 5%, 2 cos (21rd cos 6/)\) 1 (glqigipl so that P=21r d cos 0A and I=(21r dB cos 0A) cos (21rft-l- Ks cos a is desired, five microphone units may be aligned as shown in Figure 8. The procedure may be continued for any degree of selectivity desired. In Figure 11 is given the data for directional systems up to and including 11 aligned units wherein the adjacent units are spaced apart a distance d" of the order of or less. Should a still higher degree of directivity be required, for example directivity proportional to Kn cos 0, the sensitivity of the a igned elements will be as follows: I' irst element: A Second element: 'nA Third element: rim-4);- r element: 1; element: 1) "WA (11-!- 1) element: 1) "A The negative signs again indicate that these elements are connected sothat their outputs are 180 out of phase with the elements having a positive sign. It will be noted that these are just coeflicients of the binomial expansion of (1-m) "A. The proof of the above expressions for the strength of the elements can be established easily as follows: Since the values are the binomial coeillcients in the expansion of (1-w) "A, the combination of two arrangements having characteristics cos in the manner specified will cause an element whose sensitivity is the coefiicient of as in 0-1:) "A to be combined with an element whose sensitivity is the coefliclent of 3V in (1-:z:) "A or with the coefiicient of x in (1-'-a:)":cA. The combined elements will, therefore, have values which are the coemcients of a: in (1 "a- (1:::) ".rA But this is equal to (l-Fr) "(1-:r)A= (1-:c) .4 The coefilcients of these will be the values for cos"+ 0, and are again binomial coefficients. Since we know that the formula holds for 11:22 and 11:3 it will hold for all positive integral values of n and we have completed the proof. For certain purposes, such as searching for airplanes and the like, it may be desirable to provide a sound receiving system having controllable directivity. The manner in which the response characteristic of a microphone array may be varied by a simple switching operation is exemplified by Figure 9 of the drawings, which illus-- trates a system of the type shown in Figure 3 to which has been added a two-position switch ll whereby the sensitivity may be changed at will to that of the basic transducer, that is illustrated by Figure 1 of the drawings. Should the system be of the type wherein an intermediate microphone is employed, having twice the sensitivity of a terminal microphone, an attenuator l3 for such intermediate microphone may be provided and a plurality of switching devices l5, I1 and I9 may be included so that when the attenuator is in circuit, the ,response of the system is proportional to Ken cos 0 and when the attenuator is disconnected the response characteristic is of the type Kb cos 0. I From the foregoing description of certain embodiments of this invention it will be obvious that it enables the obtaining of a high degree of directivity through the utilization of pressure actuated microphones of the most simple type and that complicated amplifiers are unnecessary. Other advantages will be apparent to those skilled in the art as well as numerous modifications and alternative embodiments of the invention. ' Although certain specific microphone-arrays have been chosen for purposes of illustration, the. invention is not to be considered as restricted thereby but it is to be limited only as is necessitated by the prior art and by the spirit of the appended claims. What is claimed is: 1. A directional sound receiving system comprising a given number of microphones, more than two, spaced apart along an axis of maximum sensitivity, the system having a plane of minimum sensitivity angularly related to said axis, the terminal microphones of the system having a given sensitivity and at least one intermediate microphone having a sensitivit greater than the given sensitivity of said terminal microphones, the said microphones being so inter-connected and so included ina common output circuit that the response of the system to sound arriving from a source disposed at an angle to the said axis is related to a power of the cosine of said angle andsaid power is a whole number greater than 1, 2. A directional sound receiving system comprising at least three microphones spaced apart along an axis of maximum sensitivity, the directional response characteristic of the system being related to the cosine of theangle raised to a power 2 or more between said axis and the direction of the sound source, and means for varying the directivity of the system. 3. A directional sound receiving system comprising at least three microphone spaced apart along an axis of maximum sensitivity, the terminal microphones each having a given sensitivity, at least one intermediate microphone having a sensitivity materially greater than said given sensitivity, and connections between said at least three microphones whereby the net response of the system is substantially zero for sound arriving from directions normal to said axis and for sound arriving from directions at an angle to said normal is related to a power of the cosine of said angle, said power being two or greater. 4. The invention set forth in claim 1, characterized in this: that the microphones are of the non directiona-l type. 5. The invention set forth in claim 2, characterized in this: that the microphones are of the non-directional type. 6. The invention set forth in claim 3, characterized in this: that the microphones are of the non-directional type. 7. A directional sound receiving system comprising at least three microphones spaced apart a given distance along an axis of maximum sensitivity, the system being adapted to the reception of a band of sound-frequencies the highest of which has a wave length more than twice said given distance, and at least one intermediate microphone having a sensitivity materially greater than the sensitivity of one of the terminal units, said microphones being so interconnected and of suflicient sensitivity that said system has a response which is related to a power of the cosine of the angle between the said direction of maxi- 'mum response and the direction of the sound and the axis of maximum sensitivity of said transducer means, second transducermeans having substantially the same directional response characteristic, each of said transducer means having a plane of minimum sensitivity substantially norfuel to said axis of maximum sensitivity, the said first and second transducer means being so oriented with respect to each other that the planes of minimum sensitivity thereof approach parallelism and are effectively spaced apart a distance of the order of, equal to or less than one eighth of the wavelength of sound at the highest frequency the system is intended to receive, the said axes approaching alignment, an output circuit, and connections for so joining the said first and second transducer means in opposed relation with respect to the output circuit that the system has an overall directional response characteristic of the type proportional to the next higher positive integral power of the cosine of the said angle. 11. The invention set forth in claim 10, char- I acterized in this: that each transd'ucer" is a pressure-gradient microphone, 14. The invention set forth in claim 10, characterized in this: that the distance by which said two transducer means are spaced apart is measured along a line substantially normal to the planes of minimum sensitivity of the transducers. 15. In a directional sound receiving system, a transducer having a directional response characteristic of the type proportional to the angle between the direction of a sound source and the axis of maximum sensitivity of said transducer, a second transducer having substantially the same directional response characteristic, the said transducers being so oriented with respect to each other that their axes of maximum sensitivity approach,coincidence and the transducers are effectively spaced apart a distance equal to or less than one half of the wavelength of sound at the highest frequency the system is intended to receive, an output circuit, and connections for so joining the transducers in opposed relation with respect to the output circuit that the system has an overall directional response characteristic of the type proportional to some power of the cosine of the said angle, said power being two or more and related to the number of transducers in said system. 16. In a directional sound receiving system, at least three microphones comprising, in effect a plurality of connected pairs of microphones each microphone having substantially the same shape of response pattern and each pair of microphones having an axis of maximum sensitivity, said at least three microphones being spaced apart and arranged in a substantially straight line with each said pair of microphones having its axis of maximum sensitivity substantially parallel to the said straight line, the terminal microphones in said straight line having a given sensitivity, and the intra-terminal microphone means having a sensitivity related to said given sensitivity in accordance with the relation between the terminal and intra-terminal terms attained by the binomial expansion of the term (tZ -b) the power of said expansion being directly related to the number of effective pairs of microphones in said straight line, said microphones being connected together in a common circuit and phased in accordance with the sign of each binomial term of the said expanded term (ab) and said microphones being so connected that the system has an overall directional response characteristic proportional to the same positive integral power of the cosine of the angle between said straight line and the direction of a sound source as the power to which saidterm (ab) was expanded. 17. The invention as set forth in claim 16 further characterized in this, that each of said microphones is substantially non-directional in character. 18. The invention as set forth in claim 16 further characterized in this, that the spacing between microphones is less than about one-fourth of the wave-length of the highest sound-frequency which the system is adapted to receive. 19. The invention as set forth in claim 16 further characterized in this, that the said system includes at least one intra-terminal microphone having a sensitivity at least twice the sensitivity of one of said terminal microphones. 20. The invention as set forth in claim 16 further characterized in this, that the said system effectively includes two pairs of microphones and the intra-terminal microphone means is substantially twice as sensitive as each of the said terminal microphone means, and the microphones are connected in such phase that the two terminal microphones are of the same phase for a given exciting sound pressure and the intra-terminal microphone means are of the opposite phase, and the said microphone means are so connected that the overall directional response characteristic is proportional to the second power of the cosine of the angle between the said straight line and the direction of a sound source. 21. The invention as set forth in claim 16 further characterized in this, that the said system effectively includes three pairs of microphones and there are two intra-terminal microphone means each of which is substantially three times as sensitive as each of the said terminal microphone means, and the microphones are connected in such phase that the'two terminal microphones are of the opposite phase for a given exciting sound pressure and the two intra-terminal microphone means are of the opposite phase for a given exciting sound pressure, and the said microphone means are so connected that the over-. all directional response characteristic is proportional to the third power of the cosine of the angle between the said straight line and the direction of a sound source. 22. In a directional sound receiving system, at least three microphones having substantially the same shape of response pattern and each having an axis of maximum sensitivity, said at least three microphones being arranged in a substantially straight line with each microphone having the axis of maximum sensitivity substantially parallel to the said straight line, each of the said Inicrophones being spaced apart from the next adjacent microphone by a distance no greater than about of a wave length of the highest frequency to be received, the said microphones having sensitivities and positions directly related to the coefiicients and position of the terms attained by the binomial expansion of the term (c-b), the power of said expans n being one 6 -s,see,sss less than the number of microphones in said line, said microphones being connected together in a common electrical circuit and phased respectively in accordance with the sign of each binomial term said straight line and the direction of a sound source as the power to which said term (a-b) was expanded. 23. The invention as set forth in claim 22, further characterized in this: that each of said Iu'; i crophones is o! the non-directional type. ' 13m L. F032. Referenced by
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