ABSTRACT 



The Wiener-Hopf technique is now firmly estab- 

 lished as a powerful tool for research in certain 

 types of boundary value, problem arising in acous- 

 tics. Typical problems which may be solved exact- 

 ly or asymptotically with this technique concern 

 the sound and vibration levels generated by finite 

 or semi-infinite planar or cylindrical surfaces, 

 of local or extended reaction, immersed in a com- 

 pressible fluid and subject to acoustic or mechan- 

 ical forcing. However, even the simplest of these 

 problems involves complications which are irrele- 

 vant to an understanding of the Wier.er-Hopf method 

 itself and its various extensions. Accordingly, 

 this report was written in an attempt to display 

 the operation of the technique in an even simpler 

 physical and mathematical context, and thereby to 

 encourage its more widespread use. The report 

 deals with the application of Wiener-Hopf methods 

 to one-dimansional wa/e motions on strings and 

 beams, and in particular with the reflection and 

 transmission from discontinuities in the mechan- 

 ical properties of a string. Also included is a 

 section illustrating how a generalized Wiener- 

 Hopf problem can be set up for a three-part prob- 

 lem involving a string of finite length. Two- 

 dimensional wave probleE3 are then exemplified in 

 a discussion of the acoustic field generated by a 

 vibrating half-plane, and the effect of uniform 

 mean flow over the half-plane is included to show 

 how different tvpes of "edge condition" nay be 

 accommodated. The final section sets out in detail 

 the properties of certain functions arising very 

 frequently in application of Wiener-Hopf methods 

 to acoustic problems. 



ADMINISTRATIVE INFORMATION 

 This work was performed under DTNSRDC Contract No. N0O167-76-M-8415, 

 financed under DTNSRDC Job Order 4-1900-001-32. At the time, the author, 

 whose permanent address is Department of Applied Mathematical Studies, 

 University of Leeds, England, was a visiting professor in the Depa rtment of 

 Mechanical Engineering, [Catholic University of America, Washington, D.C. 



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