Advertisement

Huygens Principle and the Rubinowicz-Kirchhoff Theory of Diffraction

  • Eugen Skudrzyk

Abstract

In discussing diffraction, we shall frequently use the language of optics and talk about a shadow boundary, an illuminated space, light sources, and screens (boffles). A block body is an ideally absorbent body. This language is natural because most of the original work has been done for light diffraction. However, there is no difference between the computations for light and for sound waves, as long as both are based on the assumption of a scalar potential. Using a scalar and a vector potential optical computations have also been performed for boundary conditiosn that apply to electrical waves. Such computations have no bearing on sound waves and are not discussed in this book.

Keywords

Incident Wave Diffract Wave Field Point Shadow Region Edge Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anders, T.: Beugung akustischer Wellen an einer kleinen kreisförmigen Öffnung. Z. Physik 135 (1953) 219–224.MathSciNetADSMATHCrossRefGoogle Scholar
  2. Andrejewski, W.: Die Beugung elektromagnetischer Wellen an der leitenden Kreisscheibe und an der kreisförmigen Öffnung. Z. angew. Physik 5 (1953) 178–185.Google Scholar
  3. Andrews, C. L.: Diffraction pattern in a circular aperture measured in the microwave region. J. Appl. Phys. 21 (1950) 761–767.ADSCrossRefGoogle Scholar
  4. Artmann, K.: Beugung polarisierten Lichtes an Blenden endlicher Dicke im Gebiet der Schattengrenze. Z. Physik 127 (1950) 468–494;MathSciNetADSMATHCrossRefGoogle Scholar
  5. Artmann, K.: Beugung an einer einbackigen Blende endlicher Dicke und der Zusammenhang mit der Theorie der Seitenversetzung des totalreflektierten Strahles. Ann. Physik 7 (1950) 209–212.ADSMATHCrossRefGoogle Scholar
  6. Atawani, J.: Diffraction of a sound wave by a circular aperture. Mem. Res. Inst. Acoust. Sci. Osaka 2 (1951) 14–20; Physics Abstr. 55 (1952) 2542.Google Scholar
  7. Atkinson, F. V.: On Sommerfeld’s “radiation condition”. Phil. Mag. (7) 40 (1949) 645–651.MATHGoogle Scholar
  8. Baars, J. W. M.: On the diffraction of sound waves by a circular disc. Acustica 14 (1964) 289.MATHGoogle Scholar
  9. Baker, B. B., Copson, E. T.: The mathematical theory of Huygens’ principle. Oxford: Clarendon Press. 1950.MATHGoogle Scholar
  10. Banaugii, R. P., Goldsmith, W.: Diffraction of steady acoustic wave by surfaces of arbitrary shape. J.A.S.A. 35 (1963) 1590.Google Scholar
  11. Barnett, J. D.: Effect of edge parameters on Fresnel diffraction of light at a straight edge. Thesis, University of Utah, April 1959.Google Scholar
  12. Bekefi, G.: Diffraction of sound waves by a circular aperture. J.A.S.A. 25 (1953) 205.Google Scholar
  13. Belle, T. S.: Allowance for the influence of the edges of a spherical radiator on the radiated field. J.A.S.A. 15 (1970) 296;Google Scholar
  14. Belle, T. S.: Analysis of a slightly convex spherical radiator in the Kirchhoff approximation. Sov. Phys. Acoust. 14 (1969) 296;Google Scholar
  15. Belle, T. S.: Application of an integral representation of the MacDonald function for computation of the Kirchhoff integral in calculating the field of a slightly convex spherical radiator. Soy. Phys. Acoust. 14 (1969) 436.Google Scholar
  16. Bickley, W. G.: The diffraction of waves by a semi-infinite screen with a straight edge. Phil. Mag. (6) 39 (1920) 668–672.Google Scholar
  17. Bobrovnikov, M. S., Starovoitova, R. P.: Diffraction of cylindrical waves by an impedance wedge. Izv. vuzov, Fizika 6 (1963) 168–176.Google Scholar
  18. Boersch, A.: Über die Gültigkeit des Babinetschen Theorems. Z. Physik 131 (1951–52) 78–81.Google Scholar
  19. Bolt, R. H, Labate, S., Ingard, U.: Acoustic reactance of small circular orifices. J.A.S.A. 21 (1949) 94.Google Scholar
  20. Booker, H. G.: Slot aerials and their relation to complementary wire aerials (Babinet’s principle). J.I. E.E. Part III A 93 (1946) 620–626.Google Scholar
  21. Bordoni, P. G.: Methodes approchées pour l’étude des sources sonores. Ric. Sci. 15 (1945) 147–148.Google Scholar
  22. Born, M., Wolf, E.: Principles of optics, electromagnetic theory of propagation, interference and diffraction of light. London—New York—Paris—Los Angeles: Pergamon Press. 1959.MATHGoogle Scholar
  23. Bouwkamp, C. J.: Note on the anomalous propagation of phase in the focus. Physica 7 (1940) 485–489;ADSMATHCrossRefGoogle Scholar
  24. Bouwkamp, C. J.: Theoretische en numericke behandeling van de buiging door een ronde opening. Diss. Groningen 1941;Google Scholar
  25. Bouwkamp, C. J.: A contribution to the theory of acoustic radiation. Philips Res. Rep. 1 (1945/46) 251–277;Google Scholar
  26. Bouwkamp, C. J.: Vibrating disk; diffraction by disks and apertures. Physica 16 (1950) 1–16;MathSciNetADSMATHCrossRefGoogle Scholar
  27. Bouwkamp, C. J.: A note on singularities occuring at sharp edges in electromagnetic diffraction theory. Phys.ca 12 (1946) 467–474; Diffraction theory. Phys. Soc. Repts. Progr. in Phys. 17 (1954) 35–100.MathSciNetADSCrossRefGoogle Scholar
  28. Braunbek, W.: Neue Näherungsmethode für die Beugung am ebenen Schirm. Z. Physik 127 (1950) 381–390;MathSciNetADSMATHCrossRefGoogle Scholar
  29. Braunbek, W.: Zur Beugung an der Kreisscheibe. Z. Physik 127 (1950) 405–415;MathSciNetADSMATHCrossRefGoogle Scholar
  30. Braunbek, W.: Zur Darstellung von Wellenfeldern. Z. Naturforsch. 6a(1951)12–15;MathSciNetADSGoogle Scholar
  31. Braunbek, W.: Zur Beugung an der kreisförmigen Öffnung. Z. Physik 138 (1954) 80–88;MathSciNetADSMATHCrossRefGoogle Scholar
  32. Braunbek, W.: Zur Beugung an Öffnungen in nichtebenen Schirmen. Z. Physik 156 (1959) 66–77.MathSciNetADSMATHCrossRefGoogle Scholar
  33. Buddruss, C., Wille, P.: Experimentelle Untersuchungen zur Wasserschallstreuung an absorbierend verkleideten Zylindern. Acustica 18 (1969) 59.Google Scholar
  34. Butrov, M. V.: Diffraction of a scalar wave by a slit and by a circular aperture in a screen of arbitrary thickness. Sov. Phys. Acoust. 6 (1960) 13.MathSciNetGoogle Scholar
  35. Carlisle, R. W.: Conditions for wide angle radiation from conical sound radiators. J.A.S.A. 15 (1943) 44–49.Google Scholar
  36. Carter, A. H., Williams, A. O., Jr.: New expansion for the velocity potential of a piston source. J.A.S.A. 23 (1951) 179–184.MathSciNetGoogle Scholar
  37. Copley, L. G.: Fundamental results concerning integral representations in acoustic radiation. Cambridge Acoustical Associates 44 (1968) 28–32.ADSMATHCrossRefGoogle Scholar
  38. Copson, E. T.: Diffraction by a plane screen. Proc. Roy. Soc. London 202 (1950) 277–284.MathSciNetADSMATHCrossRefGoogle Scholar
  39. Coquard, A.: Application du principle d’Huygens au calcul du rayonnement sonore des transformateurs. Acustica 17 (1966) 285.Google Scholar
  40. Courant, R, Hilbert, D.: Methoden der mathematischen Physik, Bd. II. Berlin: Springer. 1937.Google Scholar
  41. Danielmeyer, H. G.: Aperture corrections for sound-absorption measurements with light scattering. J.A.S.A. 47 (1970) 151.Google Scholar
  42. Debye, P.: Das Verhalten von Lichtwellen in der Nähe eines Brennpunktes oder einer Brennlinie Ann. Physik (4) 30 (1909) 755–776.ADSCrossRefGoogle Scholar
  43. Dumery, G.: Sur la diffraction des ondes sonores par des grilles ou des reseaux d’obstacles. Acustica 18 (1967) 334.Google Scholar
  44. Esche, V.: Experimentelle Untersuchungen zu Einflußparametern und Größe des Kanteneffektes. Acustica 19 (1967–68) 301.Google Scholar
  45. Fox, E. N.: The diffraction of sound pulses by an infinitely long strip. Proc. Roy. Soc. A 241 (1948) 71–103;MATHGoogle Scholar
  46. Fox, E. N.:The diffraction of two-dimensional sound pulses incident on an infinite uniform slit in a perfectly reflecting screen. Phil. Trans. A 242 (1949) 1–32.ADSMATHCrossRefGoogle Scholar
  47. Frank, P., Mises, R. v.: Die Differential-und Integralgleichungen der Mechanik und Physik, II. Braunschweig: Vieweg. 1935.Google Scholar
  48. Franz, W.: Zur Theorie der Beugung. Z. Physik 125 (1949) 563–596;MathSciNetADSMATHCrossRefGoogle Scholar
  49. Franz, W.: On the theory of diffraction. Proc. Physic. Soc. London A 63 (1950) 925–939;MathSciNetADSCrossRefGoogle Scholar
  50. Franz, W.: Zur Formulierung des Huygensschen Prinzips Z Naturforsch. 3a (1948) 500–506;MathSciNetMATHGoogle Scholar
  51. Franz, W.: Zur Theorie der Beugung am Schirm. Z. Physik 128 (1950) 432–441.MathSciNetADSMATHCrossRefGoogle Scholar
  52. Fraunhofer, J. Von: Neue Modifikation des Lichtes durch gegenseitige Einwirkung und Beugung der Strahlen, und Gesetze derselben. Denkschr. Münchner Akad. 8 (1822) 1;Google Scholar
  53. Fraunhofer, J. Von: Schuhmachers astr. Abhandl. Bd. 2, 1823; Gilberts Ann. 74 (1823) 337;Google Scholar
  54. Fraunhofer, J. Von: auch Gesammelte Schriften, herausg. von E. Lommel, S. 51. München: Verl. Bayer. Akad. Wiss. 1888.Google Scholar
  55. Fredricks, R. W.: Diffraction of an elastic pulse in a loader half-space. J.A.S.A. 33 (1961) 17.MathSciNetGoogle Scholar
  56. Fresnel, A.: Oeuvres complètes d’Augustin Fresnel publiées par MM. Henri de Senarmont, Emile Verdet et Léonor Fresnel, Tome I. Paris: Imprimerie Impériale. 1866.Google Scholar
  57. Friedlander, F. G.: On the half-plane diffraction problem. Quart. J. Mech. Appl. Math. 4 (1951) 344–357; Sound pulses. Cambridge: University Press. 1958.Google Scholar
  58. Friedlander, F. O.: The diffraction of sound pulses I. Diffraction by a semi-infinite plane. Proc. Roy. Soc. London 186 (1946) 322–344;ADSMATHCrossRefGoogle Scholar
  59. Friedlander, F. O.:The diffraction of sound pulses II. Diffraction by an infinite wedge. Proc. Roy. Soc. London 186 (1946) 344–351;ADSCrossRefGoogle Scholar
  60. Friedlander, F. O.:The diffraction of sound pulses III. Note on an integral occurring in the theory of diffraction by a semi-infinite screen. Proc. Roy. Soc. London 186 (1946) 352–355.ADSCrossRefGoogle Scholar
  61. Friedman, M. B.: The method of Green’s function applied to the diffraction of pulses by wedges. Techn. Rep. 18, Dept. of Civil Eng and Eng. Mech., Columbia Univ., Nov. 1956.Google Scholar
  62. Gerjuoy, E.: Refraction of waves from a point source into a medium of higher velocity. Physic. Rev. 73 (1948) 1442–1449.MathSciNetADSMATHCrossRefGoogle Scholar
  63. Ghen, L. H., Schweikert, D. G.: Sound radiation from an arbitrary body. J.A.S.A. 35 (1963) 1626.Google Scholar
  64. Gitis, M. B., Khimunin, A. S.: Diffraction effects in ultrasonic measurements (review). Soy. Phys. Acoust. 14 (1969) 413.Google Scholar
  65. Guptill, E. W.: The sound field of a piston source. Can. J. Physics 31 (1953) 394–401.MathSciNetADSCrossRefGoogle Scholar
  66. Heaps, H. S.: Diffraction of an acoustical wave obliquely incident upon a circular disk. J.A.S.A. 26 (1954) 707.Google Scholar
  67. Hönl, H.: Eine strenge Formulierung des klassischen Beugungsproblems. Z. Physik 131 (1951–52) 290 304.Google Scholar
  68. Hönl, H., Made, A. W., Westpfahl, K.: Theorie der Beugung. Handbuch d. Phys., Bd. XXV /1, S. 218–573. Berlin—Göttingen—Heidelberg: Springer. 1961.Google Scholar
  69. Hönl, H., Maui;, A. W.: Die Eindeutigkeit der Lösungen in der strengen Beugungstheorie. Z. Physik 130 (1951) 569–578.Google Scholar
  70. Hönl, H., Westpfahl, K.: Fortentwicklung der Kirchhoffschen Beugungstheorie zu einer strengen Theorie. Max-Planck-Festschrift 1958, S. 35–64. Berlin: Deutscher Verlag der Wissenschaften. 1958.Google Scholar
  71. Hönl, H., Zimmer, E.: Intensität und Polarisation bei der Beugung elektromagnetischer Wellen am Spalt. Z. Physik 135 (1953) 196 218.Google Scholar
  72. Hosemann, R., Joerchel, D.: Die notwendige Korrektion am Babinetschen Theorem. Z. Physik 138 (1954) 209–221.ADSMATHCrossRefGoogle Scholar
  73. House, R. N., Jr.: Maximum power criterion for the vibrating free edge disk. J.A.S.A. 33 (1961) 561.Google Scholar
  74. Hutchins, D. L., Kouyoumjian, R. G.: Calculation of the field of a baffled array by the geometrical theory of diffraction. J.A.S.A. 45 (1969) 485–492.Google Scholar
  75. Huygens, C.: Traité de la lumière où sont expliquées les causes de ce que luy arrive dans la réflexion et dans la réfraction. 1690.Google Scholar
  76. Jones, D. S.: Note on diffraction by an edge. Quart. J. Mech. Appl. Math. 3 (1950) 420–434;MathSciNetMATHCrossRefGoogle Scholar
  77. Jones, D. S.: Removal of an inconsistency in the theory of diffraction. Proc. Cambridge Phil. Soc. 48 (1952) 733–741;MATHGoogle Scholar
  78. Jones, D. S.: Diffraction by a thick semi-infinite plate. Proc. Roy. Soc. London 217 A (1953) 153–175;ADSGoogle Scholar
  79. Jones, D. S.: A new method of calculating scattering, with particular reference to the circular disc. Comm. pure appl. Math. 9 (1956) 713–746.MATHGoogle Scholar
  80. Jones, D. S., Kline, M.: Asymptotic expansion of multiple integrals and the method of stationary phase. J. Math. Physics 37 (1958) 1–28.MathSciNetMATHGoogle Scholar
  81. Jones, R. C.: On the theory of the directional patterns of continuous source distributions on a plane surface. J.A.S.A. 16 (1945) 147–171.Google Scholar
  82. Jusofie, M. J.: Schallrichtungsverteilung im Hallraum bei 2000 Hz und Kantenbeugung an absorbierenden Materialien. Acustica 13 (1963) 280.Google Scholar
  83. Kampen, N. G. Van: An asymptotic treatment of diffraction problems. Physica 14 (1949) 575–589; The method of stationary phase and the method of Fresnel zones. Physica 24 (1958) 437–444.MathSciNetADSMATHCrossRefGoogle Scholar
  84. Karnovskii, M. I., Lozovlx, V. G.: Sound field of a space radiator of arbitrary configuration under mixed boundary conditions. Sov. Phys. Acoust. 14 (1969) 336.Google Scholar
  85. Keller, J. B.: Diffraction by a convex cylinder. I.R. E. Trans. 4 (1956) 312–321;Google Scholar
  86. Keller, J. B.: Diffraction by an aperture. J. Appl. Physics 28 (1957) 426–444;ADSMATHCrossRefGoogle Scholar
  87. Keller, J. B.: A geometrical theory of diffraction. Calculus of Variations and its Applications. New York, Toronto, London: McGraw-Hill 1958;Google Scholar
  88. Keller, J. B.: How dark is the shadow of a round-ended screen ? J. Appl. Physics 30 (1959) 1452–1454;ADSCrossRefGoogle Scholar
  89. Keller, J. B.: Geometrical theory of diffraction. J. Opt. Soc. Am. 52 (1962) 116–130;ADSCrossRefGoogle Scholar
  90. Keller, J. B.: Diffraction by polygonal cylinders. Electromagnetic Waves. Madison: The Univ. of Wisconsin Press. 1962.Google Scholar
  91. Keller, J. B., Ahluwalia, D. S.: Progressing waves diffracted by smooth surfaces. J. Math. Mech. 19 (1969) 515–530.MathSciNetMATHGoogle Scholar
  92. Kharkevich, A. A.: A new method for solving diffraction problems. Dokl. Akad. Nauk. SSSR 72 (1950) 45–47.MATHGoogle Scholar
  93. Khaskind, M. D.: Propagation of acoustic and electromagnetic waves in a half space. Sov. Phys. Acoust. 5 (1960) 476.Google Scholar
  94. King, L. V.: On the acoustic radiation field of the piezoelectric oscillator and the effect of viscosity on the transmission. Canad. J. Research 11 (1934) 135–155, 484–488.CrossRefGoogle Scholar
  95. King, R. W. P., Tai Tsux Wu: The scattering and diffraction of waves. Cambridge, Mass.: Harvard Univ. Press. 1959.Google Scholar
  96. Kirchhoff, G.: Zur Theorie der Lichtstrahlen. Sitz.-Ber. kgl. preuß. Akad. Wiss. 22. Juni 1882, S. 641;Google Scholar
  97. Kirchhoff, G.:Wied. Ann. Physik 18 (1883) 663; Ges. Abhandl. Nachtrag, S. 22–54. Leipzig: Barth. 1891;Google Scholar
  98. Kirchhoff, G.:Vorlesungen über mathematische Optik, herausg. v. K. HENSEL. Leipzig: Teubner. 1891.Google Scholar
  99. Kleinman, R. E.: Integral representations of solutions of the Helmholtz equation with application to diffraction by a strip. Diss. Techn. Hogeschool to Delft. 1961;Google Scholar
  100. Kleinman, R. E.: Plane wave diffraction by a strip. Electromag. Theory and Antennas, Pergamon Press. 1963.Google Scholar
  101. Kocx, E., Harvey, F. K.: Refracting sound waves. J.A.S.A. 21 (1949) 471–481.Google Scholar
  102. Korn, T. S.: Étude des différents baffles acoustiques pour hautparleurs. Toute la Radio 17 (1950) 183–186; Ann. Télécom. 5 (1950) 33070.Google Scholar
  103. Kossel, W.: Zur Lichtbeugung. Z. Naturforsch. 3a (1948) 496–500;ADSGoogle Scholar
  104. Kossel, W.:Didaktisches zur Lichtbeugung. Z. Naturforsch. 4 a (1949) 506–509.Google Scholar
  105. Kossel, W., Strohmaielt, K.: Zum Elementarvorgang der Lichtbeugung. Z. Naturforsch. 6a (1951) 504–508.ADSGoogle Scholar
  106. Kottler, F.: Zur Theorie der Beugung an schwarzen Schirmen. Ann. Physik 70 (1923) 405 456;Google Scholar
  107. Kottler, F.: Elektromagnetische Theorie der Beugung an schwarzen Schirmen. Ann. Physik (4) 71 (1923) 457–508.CrossRefGoogle Scholar
  108. Krom, M. N., Cxernoy, L. A.: The effect of fluctuations in the incident wave on the mean intensity distribution in the vicinity of the focus of the lens. Soy. Phys. Acoust. 4 (1958) 352.Google Scholar
  109. Kuhl, W.: Der Einfluß der Kanten auf die Schallabsorption poröser Materialien. Acustica 10 (1960) 264.Google Scholar
  110. Kujawski, A.: Reciprocity theorems and Babinet’s principle in Kirchhoff’s theory of the diffraction of electromagnetic waves. Acta Phys. Polon. 21 (1962) 597–607;MathSciNetGoogle Scholar
  111. Kujawski, A.:On the Kirchhoff Young diffraction theory of electromagnetic waves. Bull. A.ad. Polonaise Sci., Sér. sci. math. astr. phys. 11 (1963) 67–72;MATHGoogle Scholar
  112. Kujawski, A.:On Kirchhoff’s solution of the electromagnetic diffraction problem. Acta Phys. Polon. 25 (1964) 7 9.Google Scholar
  113. Kuttruff, H., Riscxbieter, F.: Modellversuche zur Schallreflexion an durchbrochenen, konkaven Flächen. Acustica 11 (1961) 238.Google Scholar
  114. Kuznetsov, V. K.: Experimental investigation of the sound field excited by a point source in a fluid wedge with compliant boundaries. Sov. Phys. Acoust. 13 (1967) 191.Google Scholar
  115. Lamb, G. L., Jr.: Diffraction of a plane sound wave by a semi-infinite thin elastic plate. J.A.S.A. 31 (1959) 929–935.MathSciNetGoogle Scholar
  116. Lamb, H.: On Sommerfeld’s diffraction problem; and on reflection by a parabolic mirror. Proc. London Math. Soc. (2) 4 (1907) 190–203; Hydrodynamics, VI. Aufl. New York, N. Y.: Dover Publication. 1945.Google Scholar
  117. Lapin, A. D.: Applicability of the Kirchhoff principle for calculation of the sound scattering by an uneven surface of a solid. Soy. Phys. Acoust. 15 (1969) 75.Google Scholar
  118. Larmor, J.: On the mathematical expression of the principle of Huygens. Proc.London Math. Soc. (2) 1 (1904) 1–13.CrossRefGoogle Scholar
  119. Laue, M. Von: Die Freiheitsgrade von Strahlenbündeln. Ann. Physik 44 (1914) 1197–1212;ADSGoogle Scholar
  120. Laue, M. Von: Interferenz und Beugung elektromagnetischer Wellen, in Wienharms, Handbuch der Experimentalphysik, Bd. 18;Google Scholar
  121. Laue, M. Von: Wellenoptik. Enzykl. d. Math. Wiss. Bd. V/3, Art. 24 (1915) 359–487. Leipzig: Teubner;Google Scholar
  122. Laue, M. Von: Interferenz und Beugung elektromagnetischer Wellen (mit Ausnahme der Röntgenstrahlen) Handbuch der Experimentalphysik, Bd. 18, 211 361. Leipzig: Akad. Verlagsges. 1928;Google Scholar
  123. Laue, M. Von: Bemerkung über Fraunhofersche Beugung. Sitz.-Ber. preuß. Akad. Wiss., Physik.-math. Kl. 1936, 89–91.Google Scholar
  124. Lax, M.: The effect of radiation on the vibrations of a circular diaphragm. J.A.S.A.16 ( 1944 45 ) 5–13.Google Scholar
  125. Leitner, A.: Diffraction of sound by a circular disc. J.A.S.A. 21 (1949) 331–334;MathSciNetGoogle Scholar
  126. Leitner, A.: Notes on diffraction by a circular disk. Mathematics Research Group. New York University, Washington Square College 1949. Report No. EM-12. Appl. Mech. Rev. 3 (1950) 2526.Google Scholar
  127. Levine, H.: Variational principles in acoustic diffraction theory. J.A.S.A. 22 (1950) 48.Google Scholar
  128. Levine, H., Schwinger, J.: On the theory of diffraction by an aperture in an infinite screen I. Physic. Rev. 74 (1948) 958–974; II. Physic. Rev. 75 (1949) 1423 1431.MathSciNetGoogle Scholar
  129. Levitas, A., Lax, M.: Scattering and absorption by an acoustic strip. J.A.S.A. 23 (1951) 316.MathSciNetGoogle Scholar
  130. Levy, B. R., Keller, J. B.: Diffraction by a smooth object. Communications on Pure and Applied Mathematics 12 (1959) 159 209.Google Scholar
  131. Lindsay, R. B.: High frequency sound radiation from a diaphragm. Physic. Rev. 32 (1928) 515 519.ADSGoogle Scholar
  132. Linfoot, E. H., Wolf, E.: Phase distribution near focus in an aberration-free diffraction image. Proc. Phys. Soc. London B 69 (1956) 823–832.ADSMATHCrossRefGoogle Scholar
  133. Lippert, W. K. R.: Measurement of sound transmission through an orifice in a duct with an application to a resonator. Acustica 8 (1958) 173.Google Scholar
  134. Lippmann, B. A.: On the Sommerfeld half-plane problem. Quart. J. Mech. Appl. Math. 18 (1960) 301–303.MathSciNetMATHGoogle Scholar
  135. Lyamshev, L. M.: Sound diffraction by a semi-infinite elastic plate in a moving medium. Sov. Phys. Acoust. 12 (1967) 291 294.Google Scholar
  136. Maey, E.: Über die Beugung des Lichtes an einer geraden, scharfen Schirmkante. Diss. Königsberg; Wied. Ann. Physik 49 (1893) 69–104;MATHCrossRefGoogle Scholar
  137. Maey, E.: Die Theorie der Beugungserscheinungen des Lichtes nach Thomas Young, ihre Geschichte und Verwertung zu einer schulgemäßen Behandlung der Lichtbeugung. Z. phys. Chem. Unterricht.17 (1904) 10 19;Google Scholar
  138. Maey, E.: Bemerkungen zu dem Manuskript: Eine eigentümliche Beugungserscheinung von K. Noack. Physik. Z. 25 (1924) 17–18;Google Scholar
  139. Maey, E.: Bemerkungen zu der Abhandlung von Friedrich Kottier „Zur Theorie der Beugung an schwarzen Schirmen“. Ann. Physik (4) 73 (1924) 16–20.CrossRefGoogle Scholar
  140. Maggi, G. A.: Sulla propagazione libera e perturbata delle onde luminose in un mezzo isotropo. Ann. di Matematica II a, 16 (1888) 21–48.CrossRefGoogle Scholar
  141. Magnus, W.: Über die Beugung elektromagnetischer Wellen an einer Halbebene. Z. Phys. 117 (1941) 168 179.Google Scholar
  142. Mairan, J. J.: De la diffraction. Mém. de l’anc. Acad. des Sci., S. 53. 1738.Google Scholar
  143. Malyuzhinets, G. D.: Certain generalizations of the method of reflections in the theory of sinusoidal wave diffraction (doctoral thesis). P. N. Lebedev Physics Institute, Academy of Sciences of the USSR. 1950;Google Scholar
  144. Malyuzhinets, G. D.: Mathematical formulation of the problem of forced vibrations in an arbitrary region. Dokl. AN SSSR (3) 78 (1951) 439;MATHGoogle Scholar
  145. Malyuzhinets, G. D.: Radiation of sound from vibrating faces of an arbitrary wedge, Part II. Soy. Phys. Acoust. 1 (1955) 240;Google Scholar
  146. Malyuzhinets, G. D.: The radiation of sound by the vibrating boundaries of an arbitrary wedge. Akust. Z. 1 (2) 144 164; 3 (1955) 226–234 [Soy. Phys. Acoust. 1 152, 240];Google Scholar
  147. Malyuzhinets, G. D.: Exact solution of the problem of plane wave diffraction by a semi-infinite elastic plate. Abstracts of the Fourth All-Union Acoustics Conference [in Russian] (Izd. AN SSSR, Moscow 1956 ), p. 45;Google Scholar
  148. Malyuzhinets, G. D.: Excitation, reflection, and emission of surface waves from a wedge with given face impedance. Dokl. AN SSSR (3) 121 (1958) 436–439 [Soviet Physics-Doklady, Vol. 3, p. 752];Google Scholar
  149. Malyuzhinets, G. D.: Developments in our concepts of diffraction phenomena (on the 130 anniversary of the death of Thomas Young). Usp. Fiz. Nauk 69 (1959) 321–334 (Sov. Phys. Usp. 69, 749 758 );Google Scholar
  150. Malyuzhinets, G. D.: Das Sommerfeld’sche Integral und die Lösung von Beugungsaufgaben in Winkelgebieten, Bericht auf dem III. Internationalen Kongreß für Akustik in Stuttgart am 7. 9. 1959. Ann. Physik (7) 6 (1960) 107–112;ADSGoogle Scholar
  151. Malyuzhinets, G. D.: Solution of the linearized problem of the diffraction of gravity waves by the surface of the water near a sloping shoreline by the method of Sommerfeld integrals. Abstracts of Reports to the All-Union Symposium on Wave Diffraction [in Russian] (Izd. AN SSSR, Moscow 1960 );Google Scholar
  152. Malyuzhinets, G. D.: Application of the Sommerfeld integral to the solution of certain problems in mathematical physics. Reports of the Fourth Mathematics Conference [in Russian] (1961);Google Scholar
  153. Malyuzhinets, G. D.: Examples of symmetrical problems involving diffraction by semitransmissive plates. Abstracts of the Second All-Union Symposium on Wave Diffraction, Gorki (1962), pp. 86–90.Google Scholar
  154. Mangulis, V.: Relation between the radiation impedance, pressure in the far field, and baffle impedance. J.A.S.A. 36 (1964) 212;Google Scholar
  155. Mangulis, V.: Radiation of sound from a circular disk with a uniform pressure distribution. Acustica 15 (1965) 98;MATHGoogle Scholar
  156. Mangulis, V.: On the effects of a non-rigid strip in a baffle on the propagation of sound. TRG Incorporated (1965), pp. 23 32; On optimum baffles. J.A.S.A. 42 (1967) 646–652.Google Scholar
  157. Marchand, E. W., Wolf, E.: Boundary diffraction wave in the domain of the Rayleigh—Kirchhoff diffraction theory. J. Opt. Soc. Am. 52 (1962) 761–767.MathSciNetADSCrossRefGoogle Scholar
  158. Maue, A. W.: Zur Formulierung eines allgemeinen Beugungsproblems durch eine Integralgleichung. Z. Physik 126 (1949) 601–618;MathSciNetADSMATHCrossRefGoogle Scholar
  159. Maue, A. W.: Komplementäre Beugungsprobleme. Z. Naturforsch. 4a (1949) 393 394;Google Scholar
  160. Maue, A. W.: Die Kantenbedingung in der Beugungstheorie elastischer Wellen. Z. Naturforsch. 7 a (1952) 387–389;Google Scholar
  161. Maue, A. W.: Die Beugung elastischer Wellen an der Halbebene. Z. angew. Math. Mech. 33 (1953) 1–10.MathSciNetMATHGoogle Scholar
  162. Mawardi, O.: On a variational principle in acoustics. Acustica 3 (1953) 187 191.MathSciNetGoogle Scholar
  163. Miles, J. W.: On acoustic diffraction through an aperture in a plane screen. Acustica (Beihefte) 2 (1952) 287 291;Google Scholar
  164. Miles, J. W.: On the diffraction of an acoustic pulse by a wedge. Proc. Roy. Soc. London A 212 (1952) 543–547.MathSciNetADSMATHCrossRefGoogle Scholar
  165. Mirimanov, R. G.: Beugung einer sphärischen elektromagnetischen Welle an einer kreisförmigen Scheibe (russisch). Doklady Akad. Nauk SSSR 61 (1948) 617 620.Google Scholar
  166. Mitra, S. K.: On Sommerfeld’s treatment of the problem of diffraction by a semiinfinite screen. Phil. Mag. (6) 37 (1919) 50 61;Google Scholar
  167. Mitra, S. K.:On the large-angle diffraction by apertures with curvilinear boundaries. Phil. Mag. (6) 38 (1919) 289 301;Google Scholar
  168. Mitra, S. K.:On a new geometrical theory of the diffraction-figures observed in the heliometer. Proc. Indian Assoc. Cultivation Sci. 6 (1920) Part I.Google Scholar
  169. Miyamoto, K., Wolf, E.: New approach to diffraction by aperture. J. Appl. Phys. Japan 29 (1960) 647–653;Google Scholar
  170. Miyamoto, K., Wolf, E.: Boundary diffraction wave in the presence of aberrations. J. Opt. Soc. Am. 51 (1961) 478;Google Scholar
  171. Miyamoto, K., Wolf, E.: Generalization of the Maggi—Rubinowicz theory of the boundary diffraction wave. Part I, A new representation of wave fields. J. Opt. Soc. Am. 52 (1962) 615–625;MathSciNetADSCrossRefGoogle Scholar
  172. Miyamoto, K., Wolf, E.: Generalization of the Maggi—Rubinowicz theory of the boundary diffraction wave. Part II, Application to Kirchhoff’s theory of diffraction. J. Opt. Soc. Am. 52 (1962) 626–637.MathSciNetADSCrossRefGoogle Scholar
  173. Morse, P. M., Rubenstein, P. J.: The diffraction of waves by ribbons and by slits. Phys. Rev. 54 (1938) 895–898.ADSMATHCrossRefGoogle Scholar
  174. Müller, R., Westphal, K.: Eine strenge Behandlung der Beugung elektromagnetischer Wellen am Spalt. Z. Physik 134 (1953) 245 263.Google Scholar
  175. Myshkin, V. G.: Diffraction of a scalar surface wave at oblique incidence on a boundary between impedance half-planes. Soy. Phys. Acoust. 12 (1967) 300 302.Google Scholar
  176. Nagoka, H.: Diffraction phenomena produced by an aperture on a curved surface. J. Coll. Sci., Imperial Univ. Japan 4 (1891) 301 322.Google Scholar
  177. Neubauer, W. G.: A summation formula for use in determining the reflection from irregular bodies. J.A.S.A. 35 (1963) 279.Google Scholar
  178. Nichols, R. H., Jr.: Effects of finite baffles on response of source with back enclosed. J.A.S.A. 18 (1946) 151–154.Google Scholar
  179. Nimura, T., Aida, Y.: On the radiation impedance of a rectangular plate with an infinitely large baffle. Sci. Rep. Res. Inst. Tohoku Univ. (1) 2 (1951) 337–347.Google Scholar
  180. Oberheitinger, F.: On asymptotic series for functions occuring in the theory of diffraction of waves by wedges. J. Math. Phys. 34 (1956) 245 255;Google Scholar
  181. Oberheitinger, F.:On the diffraction and reflection of waves and pulses by wedges and corners. J. Res. Nat. Bur. Stand. 61 (1958) 343 365.Google Scholar
  182. Obermeieu, F.: Berechnung aerodynamisch erzeugter Schallfelder mittels der Methode der „Matched Asymptotic Expansions“. Acustica 18 (1967) 238.Google Scholar
  183. Ott, H.: Die Sattelpunktsmethode in der Umgebung eines Poles mit Anwendung auf die Wellenoptik und Akustik. Ann. Physik (5) 43 (1943) 393–403.MathSciNetMATHCrossRefGoogle Scholar
  184. Pachner, J.: Pressure distribution in the acoustical field excited by a vibrating plate. J.A.S.A. 21 (1949) 617–625;MathSciNetGoogle Scholar
  185. Pachner, J.:On the acoustical radiation of an emitter vibrating freely in a infinite wall. J.A.S.A. 23 (1951) 185–198;MathSciNetGoogle Scholar
  186. Pachner, J.:On the acoustical radiation of an emitter vibrating freely or in a wall of finite dimensions. J.A.S.A. 23 (1951) 198–208.MathSciNetGoogle Scholar
  187. Pekeris, C. L.: Theory of propagation of sound in a half space of variable sound velocity under conditions of a shadow zone. J.A.S.A. 18 (1946) 295 315.MathSciNetMATHGoogle Scholar
  188. Petykiewicz, J.: The diffracted wave near the boundary of shadow in the case of an incident wave fulfilling the eiconal equation. Acta Phys. Polon. 26 (1964) 229–234;MathSciNetGoogle Scholar
  189. Petykiewicz, J.: Huygens’ principle for elastic waves. Acta Phys. Polon. 30 (1966) 223–236.Google Scholar
  190. Pinney, E.: A theorem of use in wave theory. J. Math. Physics 30 (1951) 1–10; Physics Abstr. 54 (1951) 9339.Google Scholar
  191. Popov, A. V.: Numerical solution of the wedge diffraction problem by the transverse diffusion method. Sov. Phys. Acoust. 15 (1969) 226;Google Scholar
  192. Popov, A. V.: Numerical solution of the problem of plane wave diffraction by the rounded edge of a semi-infinite plate. Sov. Phys. Acoust. 14 (1969) 527–529.Google Scholar
  193. Poritsky, H.: Extension of Weyl’s integral for harmonic spherical waves to arbitrary wave shapes. Commun. Pure Appl. Math. 4 (1951) 43 60.Google Scholar
  194. Pridmore-Brown, D. C., Ingard, U.: Sound propagation into the shadow zone in a temperature-stratified atmosphere above a plane boundary. J.A.S.A. 27 (1955) 36.Google Scholar
  195. Primakoff, H., Klein, M. J., Keller, J. B, Carstensen, E. L.: Diffraction of sound around a circular disc. J.A.S.A. 19 (1947) 132–142.MathSciNetGoogle Scholar
  196. Pritchard, R. L.: Optimum directivity patterns for linear point arrays. J.A.S.A. 25 (1953) 879 891;Google Scholar
  197. Pritchard, R. L.: Approximate calculatin of the directivity factor of linear point arrays. J.A.S.A. 25 (1953) 1010–1011.Google Scholar
  198. Raman, Sir C. V.: Lectures on physical optics, Part I, Bangalore. The Indian Academy of Sciences 1959; Caustics formed by diffraction and the geometric theory of diffraction patterns. The Indian Academy of Sciences. A 49 (1959) 307–317.MathSciNetMATHGoogle Scholar
  199. Rayleigh, Lord: On the passage of waves through apertures in plane screens and allied problems. Philos. Mag. 43 (1897) 259–272.Google Scholar
  200. Rubinowicz, A.: Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen. Ann. Physik (4) 53 (1917) 257–278;CrossRefGoogle Scholar
  201. Rubinowicz, A.: Herstellung von Lösungen gemischter Randwertprobleme bei hyperbolischen Differentialgleichungen zweiter Ordnung durch Zusammenstückelung aus Lösungen einfacherer gemischter Randwertaufgaben. Monatsh. Math. Phys. 30 (1920) 65 79;Google Scholar
  202. Rubinowicz, A.: Zur Kirchhoffschen Beugungstheorie. Ann. Physik (4) 73 (1924) 339–364;CrossRefGoogle Scholar
  203. Rubinowicz, A.: Bemerkungen zur Arbeit von F. Kottler: „Zur Theorie der Beugung an schwarzen Schirmen“. Ann. Physik (4) 74 (1924) 459–460;CrossRefGoogle Scholar
  204. Rubinowicz, A.: Zur Theorie der Beugung an schwarzen Schirmen. Ann. Physik (4) 81 (1926) 140–164;MATHCrossRefGoogle Scholar
  205. Rubinowicz, A.: Über die Eindeutigkeit der Lösung der Maxwellschen Gleichungen. Physik. Z. 27 (1926) 707–710;Google Scholar
  206. Rubinowicz, A.: Zur Integration der Wellengleichung auf Riemannschen Flächen. Math. Ann. 96 (1927) 648–687;MathSciNetMATHCrossRefGoogle Scholar
  207. Rubinowicz, A.: On the anomalous propagation of phase in the focus. Phys. Rev. 54 (1938) 931–936;ADSMATHCrossRefGoogle Scholar
  208. Rubinowicz, A.: Eine einfache Ableitung des Ausdruckes für die Kirchhoffsche Beugungswelle. Acta Phys. Polon. 12 (1953) 225–229;MATHGoogle Scholar
  209. Rubinowicz, A.: Die Rolle der Beugungswelle in den Fraunhoferschen Beugungserscheinungen. Acta Phys. Polon. 13 (1954) 3–13;MathSciNetMATHGoogle Scholar
  210. Rubinowicz, A.: JJber eine Verallgemeinerung des Reziprozitätstheorems für Lösungen der Schwingungsgleichung mit Multipolquellen. Acta Phys. Polon. 14 (1955) 183 190;Google Scholar
  211. Rubinowicz, A.: Phasensprung im Brennpunkt. Acta Phys. Polon. 20 (1961) 357–367;Google Scholar
  212. Rubinowicz, A.: Reziprozitätstheorem und Babinetsches Prinzip in der Kirchhoffschen Theorie der Beugung. Acta Phys. Polon. 20 (1961) 725 735;Google Scholar
  213. Rubinowicz, A.: Beugungswelle im Falle einer beliebigen einfallenden Lichtwelle. Acta Phys. Polon. 21 (1962) 61 87;Google Scholar
  214. Rubinowicz, A.: Eindeutigkeitsbeweis für das elektromagnetische Sprungwertproblem. Acta Phys. Polon. 21 (1962) 415–422;Google Scholar
  215. Rubinowicz, A.: Über eine einfache Ableitung der mit der Lösung des Sommerfeldschen Beugungsproblems verknüpften Vektorpotentiale. Acta Phys. Polon. 28 (1965) 737 747;Google Scholar
  216. Rubinowicz, A.: Darstellung der Sommerfeldschen Beugungswelle in einer Gestalt, die die Beiträge der einzelnen Elemente der beugenden Kante zur gesamten Beugungswelle erkennen läßt. Acta Phys. Polon. 28 (1965) 841–860.MathSciNetGoogle Scholar
  217. Sakharova, M. P.: Asymptotic representation of the sound field of a point source in a wedge-shaped region. Soy. Phys. Acoust. 5 (1959) 214;Google Scholar
  218. Rubinowicz, A.: Influence of a wedge with vibrating faces on the radiated acoustic power. Sov. Phys. Acoust. 12 (1966) 60–66.Google Scholar
  219. Sasao, M.: Reflection of a sound wave from a circular plate. Proc. Physic. Math. Soc. Japan 14 (1932) 510–521.Google Scholar
  220. Schelkunoff, S. A.: A mathematical theory of linear arrays. B.S.T.J. 22 (1943) 80–107.MathSciNetMATHGoogle Scholar
  221. Schenck, H. A.: Improved integral formulation for acoustic radiation problems. J.A.S.A. 44 (1968) 41–58.Google Scholar
  222. Schilz, W.: Richtcharakteristik der Schallabstrahlung einer durchströmten Offnung. Acustica 17 (1966) 364.Google Scholar
  223. Schmitt, H. J.: Diffraction of electromagnetic waves by sound waves. J.A.S.A. 33 (1961) 1288.Google Scholar
  224. Schäfer, C.: Einführung in die theoretische Physik, Bd. III. Berlin—Leipzig: de Gruyter. 1929.Google Scholar
  225. Scheffers, H.: Vereinfachte Ableitung der Formeln für die Fraunhoferschen Beugungserscheinungen. Ann. Physik 41 (1942) 211–215.MathSciNetADSCrossRefGoogle Scholar
  226. Schelkunoff, S. A.: Field equivalence theorems. Commun. Pure Appl. Math. 4 (1951) 43 59.Google Scholar
  227. Schoch, A.: Betrachtungen über das Schallfeld einer Kolbenmembran. Akust. Z. 6 (1941) 318 326;MathSciNetGoogle Scholar
  228. Schoch, A.: Schallreflexion, Schallbrechung und Schallbeugung. Ergebnisse der exakten Naturwissenschaften XXIII (1950) 127–234.Google Scholar
  229. Seckler, B. D., Keller, J. B.: Geometrical theory of diffraction in inhomogeneous media. J.A.S.A. 31 (1959) 192;MathSciNetGoogle Scholar
  230. Seckler, B. D., Keller, J. B.: Asymptotic theory of diffraction in inhomogeneous media. J.A.S.A. 31 (1959) 206.MathSciNetGoogle Scholar
  231. Seki, H., Granato, A., Truell, R.: Diffraction effects in the ultrasonic field of a piston source and their importance in the accurate measurement of attenuation. J.A.S.A. 28 (1956) 230.Google Scholar
  232. Severin, H.: Zur Theorie der Beugung elektromagnetischer Wellen. Z. Physik 129 (1951) 426–439.MathSciNetADSMATHCrossRefGoogle Scholar
  233. Severin, H., Starke, C.: Beugung von Schallwellen an der kreisförmigen Offnung im schallharten Schirm. Acustica, A. B. 2 (1952) 59–66.Google Scholar
  234. Shifrin, Y. S.: Effect of fluctuations in the incident wave on the diffraction patterns in the focal plane of a lens. Soy. Phys. Acoust. 7 (1961) 195–200.Google Scholar
  235. Sieger, B.: Die Beugung einer ebenen elektrischen Welle an einem Schirm von elliptischem Querschnitt. Ann. Physik 27 (1908) 626–664.ADSMATHCrossRefGoogle Scholar
  236. Silberstein, L.: Über elektromagnetische Unstetigkeitsflächen und deren Fortpflanzung. Ann. Physik (4) 26 (1908) 751–762;Electrycznoéé i magnetyzm, Tome II (polnisch). Warszawa: E. Wende i S-ka.Google Scholar
  237. Sivian, L. J., O’Neil, H. T.: On sound diffraction caused by rigid circular plate, square plate, and semi-infinite screen. J.A.S.A. 3 (1932) 483–510.Google Scholar
  238. Skavlen, S.: On the diffraction of scalar plane waves by a slit of infinite length. Arch. Math. Naturw. 51 (1951) 61–80.Google Scholar
  239. Sommerfeld, A.: Analytische Theorie der Wärmeleitung. Math. Ann. 45 (1894)263–277;MathSciNetCrossRefGoogle Scholar
  240. Sommerfeld, A.: Zur mathematischen Theorie der Beugungserscheinungen. Nachr. Ges.Wiss. Göttingen, Math.-physik. Kl. 1894, 338 342;Google Scholar
  241. Sommerfeld, A.: Zur Integration der partiellen Differentialgleichung 4u k 2 u = 0 auf Riemannschen Flächen. Nachr. Ges. Wiss. Göttingen, Math.-physik. Kl. 1895, 267–274;Google Scholar
  242. Sommerfeld, A.: Mathematische Theorie der Diffraction. Math. Ann. 47 (1896) 317 374;Google Scholar
  243. Sommerfeld, A.: Über verzweigte Potentiale im Raume.Proc. London Math. Soc. 28 (1897) 395 429;Google Scholar
  244. Sommerfeld, A.: Diffractionsprobleme in exakter Behandlung. J.-Ber. Deutsch. Math.-Verein. 1894 95, 4 (1897) 172 174Google Scholar
  245. Sommerfeld, A.: Über die Ausbreitung der Wellen in der drahtlosen Telegraphie. Ann. Physik 28 (1909) 665 737;Google Scholar
  246. Sommerfeld, A.: Die Greensche Funktion der Schwingungsgleichung. J.-Ber. Deutsch. Math.-Verein. 21 (1912) 309–353;MATHGoogle Scholar
  247. Sommerfeld, A.: Theorie der Beugung, Kap. XIII in P. Frank u. R. v. Mises Differential-und Integralgleichungen der Physik, Bd. II, II. Aufl., Braunschweig: Vieweg. 1934;Google Scholar
  248. Sommerfeld, A.: Die frei schwingende Kolbenmembran. Ann. Physik (5) 42 (1942) 389 420;Google Scholar
  249. Sommerfeld, A.: Lectures on theoretical physics, 6, Partial differential equations of physics, 5, Optics. New York, N. Y.: Dover Publication. 1967;Google Scholar
  250. Sommerfeld, A.: Vorlesungen über theoretische Physik, Bd. IV, Optik, Bd. VI, Partielle Differentialgleichungen, 2. Aufl. bearbeitet und ergänzt von Fritz Bopp und Josef Meixner. Leipzig: Akad. Verlagsges. Geest and Portig. 1959.Google Scholar
  251. Spence, R. D.: Diffraction of sound by circular discs and apertures. A note on Kirchhoff approximation in diffraction theory. J.A.S.A. 20 (1948) 380–386; 21(1949) 98–100;Google Scholar
  252. Spence, R. D.: A note on the Kirchhoff approximation in diffraction theory.J.A.S.A. 21 (1949) 98–100.Google Scholar
  253. Starovoitova, R. P., Bobrovnikov, M. S., Kislitsina, V. N.: Diffraction of a surface wave by a discontinuity in an impedance plane. Radiotekhn. i élektron. 7 (2) (1962) 250;Google Scholar
  254. Starovoitova, R. P., Bobrovnikov, M. S., Kislitsina, V. N.: Excitation of an impedance wedge by a filamentary magnetic source located at the vertex. Izv. vuzov, Fizika 4 (1962) 130.Google Scholar
  255. Stratton, J. A.: Electromagnetic theory. New York and London: McGraw-Hill 1941.MATHGoogle Scholar
  256. Stenzel, H.: Über die Richtwirkung von Schallstrahlern. E.N.T. 4 (1927) 239–253;Google Scholar
  257. Stenzel, H.: Über die Richtwirkung von in einer Ebene angeordneten Strahlern. E.N.T. 6 (1929) 165–181;Google Scholar
  258. Stenzel, H.: Interferenzen durch Kolbenmembranen von besonderer Form. Z. techn. Physik 10 (1929) 567–569;Google Scholar
  259. Stenzel, H.: Über die akustische Strahlung von Membranen. Ann. Physik 7 (1930) 947–982;Google Scholar
  260. Stenzel, H.: Über die Berechnung und Bewertung der Frequenz-kurven von Membranen. E.N.T. 7 (1930) 87–99;Google Scholar
  261. Stenzel, H.: Über die Berechnung des Schallfeldes einer kreisförmigen Kolbenmembran. E.N.T. 12 (1935) 16 30;Google Scholar
  262. Stenzel, H.: Leitfaden zur Berechnung von Schallvorgängen. Berlin: Springer. 1939;Google Scholar
  263. Stenzel, H.: Über die Berechnung des Schallfeldes unmittelbar vor einer kreisförmigen Kolbenmembran. Ann. Physik 41 (1942) 245–260;MathSciNetADSCrossRefGoogle Scholar
  264. Stenzel, H.: Über die Berechnung des Schallfeldes von kreisförmigen Membranen in starrer Wand. Ann. Physik 4 (1949) 303 324;MathSciNetGoogle Scholar
  265. Stenzel, H.: Die akustische Strahlung der rechteckigen Kolbenmembran. Acustica 2 (1952) 263–281.MathSciNetGoogle Scholar
  266. Stephens, R. W. B., Bate, A. E.: Wave motion and sound. London: E. Arnold and Co. 1950.Google Scholar
  267. Storruste, A., Wergeland, H.: On two complementary diffraction problems. I. Circular hole and disc in confocal coordinates. II. Transmission of sound through a circular hole. Norske Vid. Selsk. Forh., Trondheim 21 (1948) 38–48;MathSciNetGoogle Scholar
  268. Storruste, A., Wergeland, H.: On two complementary diffraction problems. I. Circular hole and disc in confocal coordinates. II. Transmission of sound through a circular hole. Norske Vid.Appl. Mech. Rev. 4 (1951) 455;Google Scholar
  269. Storruste, A., Wergeland, H.: On two complementary diffraction problems. Physic. Rev. 73 (1948) 1397–1398.ADSMATHCrossRefGoogle Scholar
  270. Strutt, M. J. O.: Beugung einer ebenen Welle an einem Spalt von endlicher Breite. Z. Physik 69 (1931) 597–617.ADSCrossRefGoogle Scholar
  271. Tartakovskii, B. D.: The phase jump at the focus of spherical beams of sound. Soy. Phys. Acoust. 7 (1961) 179 (228).MathSciNetGoogle Scholar
  272. Theimer, O., Wassermann, G. D., Wolf, E.: On the foundation of the scalar diffraction theory of optical imaging. Proc. Roy. Soc. London A 212 (1952) 426 458.Google Scholar
  273. Torvik, P. J.: Reflection of wave trains in semi-infinite plates. J.A.S.A. 41 (1967) 346.Google Scholar
  274. >Überall, H., Doolittle, R. D., Mcnicholas, J. V.: Use of sound pulses for a study of circumferential waves. J.A.S.A. 39 (1966) 564–578.Google Scholar
  275. Voigt, W.: Kompendium der theoretischen Physik, Bd. II. Leipzig: Veit und Comp. 1896;Google Scholar
  276. Voigt, W.: Theorie der Beugung ebener inhomogener Wellen an einem geradlinig begrenzten, unendlichen und absolut schwarzen Schirm. Nachr. Akad. Wiss. Göttingen, Math.-physik. Kl. 1899.Google Scholar
  277. Waser, J., Schomaker, V.: Fourierinversion of diffraction data. Rev. Mod. Physics 25 (1953) 671–690.ADSMATHCrossRefGoogle Scholar
  278. Waterhouse, R. V.: Diffraction effects in a random sound field. J.A.S.A. 35 (1963) 1610.Google Scholar
  279. Watson, B.: Radiation loading of a piston source in a finite circular baffle. J.A.S.A. 24 (1952) 225–228.Google Scholar
  280. Weyl, H.: Ausbreitung elektromagnetischer Wellen über einen ebenen Leiter. Ann. Physik 60 (1919) 481–500.ADSMATHCrossRefGoogle Scholar
  281. Whittaker, E. T., Watson, G. N.: A course of modern analysis, 4th ed. Cambridge: University Press. 1952.Google Scholar
  282. Wiener, F. M.: Diffraction of sound by rigid discs and rigid square plates. J.A.S.A.21 (1949) 334 347;Google Scholar
  283. Wiener, F. M.: Notes on sound diffraction by rigid circular cones. J.A.S.A.20 (1948) 367 369;Google Scholar
  284. Wiener, F. M.: On the relation between the sound fields radiated and diffracted by plane obstacles. J.A.S.A. 23 (1951) 697–700.Google Scholar
  285. Willard, G. W.: Ultrasonic absorption and velocity measurements in numerous liquids. J.A.S.A. 12 (1941) 438 448.Google Scholar
  286. Williams, A. O.: Acoustic intensity distribution from a “piston” source. II. The concave piston. J.A.S.A. 17 (1946) 219 227; Piston source at high frequencies. J.A.S.A. 23 (1951) 1–6.Google Scholar
  287. Wilson, G. P., Soroxa, W. W.: Approximation of the diffraction of sound by a circular aperture in a rigid wall of finite thickness. J.A.S.A. 37 (1965) 286.Google Scholar
  288. Wolf, E.: Light distribution near focus in an error-free diffraction image. Proc. Roy. Soc. London A 204 (1951) 533–548.ADSMATHCrossRefGoogle Scholar
  289. Wolff, J., Malter, L.: Sound radiation from a system of vibrating circular diaphragms. Physic. Rev. 33 (1929) 282 Abstr.Google Scholar
  290. Yildiz, M., Mawardi, O. K.: On the diffraction of multipole fields by a semi-infinite rigid wedge. J.A.S.A. 32 (1960) 1685.MathSciNetGoogle Scholar
  291. Young, T.: A course of lectures on natural philosophy and mechanical arts. London 1807;Google Scholar
  292. Young, T.:Miscellaneous works of the late Thomas Young M. D., F. R. S., andc., and one of the eight foreign associates of the National Institute of France; Vol. I, edited by George Peacock, London: John Murray. 1855.Google Scholar
  293. Zavadsxrr, V. Y.: Certain diffraction problems in contiguous liquid and elastic wedges. Sov. Phys. Acoust. 12 (1966) 170 179.Google Scholar
  294. Zavadsxrr, V. Y., Sakuarova, M. P.: Application of special function v~ (z) in problems of wave diffraction in wedge-shaped regions. Soy. Phys. Acoust. 13 (1967) 48;Google Scholar
  295. Zavadsxrr, V. Y., Sakuarova, M. P.: Tables of the special function T o (z), Report of the Institute of Acoustics, Academy of Sciences of the USSR. Moscow 1960.Google Scholar
  296. Zernike, F.: Diffraction and optical image formation. Proc. Physic. Soc. London 61 (1948) 158–164.ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1971

Authors and Affiliations

  • Eugen Skudrzyk
    • 1
  1. 1.Ordnance Research Laboratory and Physics DepartmentThe Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations