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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Evanescent liquid-sound-pressure waves (2).*From*: "reinifrosch@xxxxxxxxxx" <reinifrosch@xxxxxxxxxx>*Date*: Sat, 10 Apr 2010 13:18:18 +0000*Approved-by*: reinifrosch@xxxxxxxxxx*Delivery-date*: Tue Apr 13 12:51:24 2010*List-archive*: <http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>*List-help*: <http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>, <mailto:LISTSERV@LISTS.MCGILL.CA?body=INFO AUDITORY>*List-owner*: <mailto:AUDITORY-request@LISTS.MCGILL.CA>*List-subscribe*: <mailto:AUDITORY-subscribe-request@LISTS.MCGILL.CA>*List-unsubscribe*: <mailto:AUDITORY-unsubscribe-request@LISTS.MCGILL.CA>*Reply-to*: reinifrosch@xxxxxxxxxx*Sender*: AUDITORY - Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

Dear colleagues,

Sorry, one more posting on the underwater tapped wine glass. I promise to stop this one-man show soon now.

A possible idealized sound-pressure function valid near the top of a submerged wine glass on its outside (i.e., for r > R, where R = radius of glass):

p = b * (R / r)^2 * cos(2phi) * cos(omega * t) ; (3)

here, b = pressure amplitude at r = R and phi = 0, pi/2, pi, and 3pi/2; r, phi = plane polar coordinates [x = r * cos(phi); y = r * sin(phi)]; omega = 2pi * frequency; t = time. Eq. (3), too, obeys the Laplace equation. Streamlines:

r = R_0 * sqrt[sin(2phi)], (4)

where R_0 is the maximal distance from center. Distance between adjacent streamlines is proportional to [1 / (liquid-particle velocity)] if R_0 for streamline number n is chosen to be as follows:

R_0 = R / sqrt(1 - n/N) , (5)

where n = 0, 1, 2, ... , N; for n = N, R_0 = infinity. The corresponding equation for the streamlines on the inside (see posting of April 8) is:

r_0 = R * sqrt(n/N) . (6).

Both inside and outside, significant liquid motion is restricted to ring-shaped zones near the glass, i.e., these standing waves really are evanescent. In "Fundamentals of Acoustics" by Kinsler et al. (Wiley, 2000), e.g., I have not found a description of such waves.

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@xxxxxxxxxx .

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