Evanescent waves in the bathtub. ("reinifrosch@xxxxxxxx" )


Subject: Evanescent waves in the bathtub.
From:    "reinifrosch@xxxxxxxx"  <reinifrosch@xxxxxxxx>
Date:    Wed, 13 Apr 2011 09:42:41 +0000
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

------=_Part_1368_1303976.1302687761584 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit Dear colleagues, Please permit me to post one more mini-tutorial. As mentioned before, evanescent (standing) liquid sound-pressure waves are the main cause of the frequency reduction observed if a drinking glass tapped with a spoon is filled with liquid. According to one model, these waves occur also during the generation of SOAEs (spontaneous oto-acoustic emissions) in the cochlea. Standing waves which are similar but have frequencies of only about one hertz can be observed in a filled bathtub. If one uses the flat hands to push the water surface down near one of the long walls, then a one-hertz oscillation can be generated. The water particles at the center of the surface oscillate horizontally. The wavelength lambda equals twice the width of the surface, i.e., lambda = 1.1 m approximately. Wave number: k = 2pi / lambda = 5.7 m^-1. If one treats this standing wave as the superposition of two travelling liquid surface waves in opposite directions, one obtains a predicted frequency of f = [1/(2pi)] * sqrt[g*k*tanh(k*H)] = 1.15 Hz; H = 0.3 m is the water depth; g = 9.8 m/s^2 is the free-fall acceleration. Reinhart. Reinhart Frosch, Dr. phil. nat., CH-5200 Brugg. reinifrosch@xxxxxxxx . ------=_Part_1368_1303976.1302687761584 Content-Type: text/html;charset="UTF-8" Content-Transfer-Encoding: quoted-printable <html><head><style type=3D'text/css'> <!-- div.bwmail { background-color:#ffffff; font-family: Trebuchet MS,Arial,Helv= etica, sans-serif; font-size: small; margin:0; padding:0;} div.bwmail p { margin:0; padding:0; } div.bwmail table { font-family: Trebuchet MS,Arial,Helvetica, sans-serif; f= ont-size: small; } div.bwmail li { margin:0; padding:0; } --> </style> </head><body><div class=3D'bwmail'><P><FONT size=3D2>Dear colleagues,</FONT= ></P> <P><FONT size=3D2>Please permit me to post one more mini-tutorial. As menti= oned before, evanescent (standing) liquid sound-pressure waves are the main= cause of the frequency reduction observed if a drinking glass tapped with = a spoon is filled with liquid. According to one model, these waves occur al= so during the generation of SOAEs (spontaneous oto-acoustic emissions) in t= he cochlea. Standing waves which are similar but have frequencies of only a= bout one hertz can be observed in a filled bathtub. If one uses the flat ha= nds to push the water surface down near one of the long walls, then a one-h= ertz oscillation can be generated. The water particles at the center of the= surface oscillate horizontally. The wavelength lambda equals twice the wid= th of the surface, i.e., lambda =3D 1.1 m approximately. Wave number: k =3D= 2pi / lambda =3D 5.7 m^-1. If one treats this standing wave as the superpo= sition of two travelling liquid surface waves in opposite directions, one o= btains a predicted frequency of<BR>f =3D [1/(2pi)] * sqrt[g*k*tanh(k*H)] = =3D 1.15 Hz;<BR>H =3D 0.3 m is the water depth; g =3D 9.8 m/s^2 is the free= -fall acceleration.</FONT></P> <P><FONT size=3D2>Reinhart.<BR><BR>Reinhart Frosch,<BR>Dr. phil. nat.,<BR>C= H-5200 Brugg.<BR>reinifrosch@xxxxxxxx . </FONT></P></div></body></html> ------=_Part_1368_1303976.1302687761584--


This message came from the mail archive
/var/www/postings/2011/
maintained by:
DAn Ellis <dpwe@ee.columbia.edu>
Electrical Engineering Dept., Columbia University