Subject: Textbook chapter on evanescent waves? From: "reinifrosch@xxxxxxxx" <reinifrosch@xxxxxxxx> Date: Mon, 12 Apr 2010 09:28:21 +0000 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>------=_Part_1202_14427053.1271064501269 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit Hello again ! The evanescent-wave liquid-sound-pressure functions near an underwater wine glass (see my postings of April 8 and 10) can be derived fairly easily with the help of analytic functions F(z) of a complex variable z = x + i * y = r * exp(i * phi). On the inside [outside] of the glass, a possible solution is obtained with F(z) = z^2 [F(z) = 1/z^2]. The sound-pressure amplitude can be identified, e.g., with const. * Re(F); then the streamlines are defined by Im(F) = const'. That analysis looks like textbook material. Up to now, I searched in "Fundamentals of Acoustics" by Kinsler et al. (Wiley, 2000, 4th ed.) and in "Hydrodynamik" by Landau and Lifschitz (Akademie Verlag, 1991, 5th ed.), without success. Suggestions would be welcome of course. Reinhart. Reinhart Frosch, Dr. phil. nat., r. PSI and ETH Zurich, Sommerhaldenstr. 5B, CH-5200 Brugg. Phone: 0041 56 441 77 72. Mobile: 0041 79 754 30 32. E-mail: reinifrosch@xxxxxxxx . ------=_Part_1202_14427053.1271064501269 Content-Type: text/html;charset="UTF-8" Content-Transfer-Encoding: 7bit <html><head><style type='text/css'> <!-- div.bwmail { background-color:#ffffff; font-family: Trebuchet MS,Arial,Helvetica; font-size: 12px; margin:0; padding:0;} div.bwmail p { margin:0; padding:0; } div.bwmail table { font-family: Trebuchet MS,Arial,Helvetica; font-size: 12px; } div.bwmail li { margin:0; padding:0; } --> </style> </head><body><div class='bwmail'><P>Hello again !</P> <P> </P> <P>The evanescent-wave liquid-sound-pressure functions near an underwater wine glass (see my postings of April 8 and 10) can be derived fairly easily with the help of analytic functions F(z) of a complex variable z = x + i * y = r * exp(i * phi). On the inside [outside] of the glass, a possible solution is obtained with F(z) = z^2 [F(z) = 1/z^2]. The sound-pressure amplitude can be identified, e.g., with const. * Re(F); then the streamlines are defined by Im(F) = const'. That analysis looks like textbook material. Up to now, I searched in "Fundamentals of Acoustics" by Kinsler et al. (Wiley, 2000, 4th ed.) and in "Hydrodynamik" by Landau and Lifschitz (Akademie Verlag, 1991, 5th ed.), without success. Suggestions would be welcome of course.</P> <P> </P> <P>Reinhart.<BR><BR>Reinhart Frosch,<BR>Dr. phil. nat.,<BR>r. PSI and ETH Zurich,<BR>Sommerhaldenstr. 5B,<BR>CH-5200 Brugg.<BR>Phone: 0041 56 441 77 72.<BR>Mobile: 0041 79 754 30 32.<BR>E-mail: reinifrosch@xxxxxxxx . </P></div></body></html> ------=_Part_1202_14427053.1271064501269--