Textbook chapter on standing liquid surface gravity waves. ("reinifrosch@xxxxxxxx" )


Subject: Textbook chapter on standing liquid surface gravity waves.
From:    "reinifrosch@xxxxxxxx"  <reinifrosch@xxxxxxxx>
Date:    Wed, 27 Apr 2011 14:38:24 +0000
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

------=_Part_2985_24757556.1303915104534 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit Dear colleagues, The low-frequency standing surface waves observable in water-filled bathtubs and in similar troughs are gravity-driven, whereas the standing evanescent liquid sound-pressure waves in water-filled drinking glasses tapped with spoons (and possibly in the human cochlea during spontaneous oto-acoustic emissions) are spring-driven. Nevertheless the two wave categories have similar streamline patterns and similar patterns of constant-pressure-amplitude lines. Therefore the low-frequency waves can be used in classroom demonstrations as introduction into the subject of evanescent liquid sound-pressure waves. The low-frequency waves are treated in a recent paper by S. J. Sinick and J. J. Lynch, "Surface Gravity Waves: Resonance in a Fish Tank", The Physics Teacher 48 (2010) 330-332. Reference 3 of that paper is the book "Hydrodynamics" by Sir Horace Lamb, 6th ed. (1932). In Chapter IX of that textbook, "Surface Waves", standing surface gravity waves in a horizontal sheet of water are discussed in detail. Eq. (11) [page 365] gives the liquid-particle displacements versus time and place for arbitrary water-sheet thickness, and in a diagram on page 366, the streamlines are shown for sheet thickness much greater than the wavelength. In the text below that diagram, it is mentioned that these waves occur in troughs if their vertical walls coincide with antinodes (where the liquid particles oscillate vertically). Reinhart. Reinhart Frosch, Dr. phil. nat., CH-5200 Brugg. reinifrosch@xxxxxxxx . ------=_Part_2985_24757556.1303915104534 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,<BR>Th= e low-frequency standing surface waves observable in water-filled bathtubs = and in similar troughs are gravity-driven, whereas the standing evanescent = liquid sound-pressure waves in water-filled drinking glasses tapped with sp= oons (and possibly in the human cochlea during spontaneous oto-acoustic emi= ssions) are spring-driven. Nevertheless the two wave categories have simila= r streamline patterns and similar patterns of constant-pressure-amplitude l= ines. Therefore the low-frequency waves can be used in classroom demonstrat= ions as introduction into the subject of evanescent liquid sound-pressure w= aves.<BR>The low-frequency waves are treated in a recent paper by S. J. Sin= ick and J. J. Lynch, "Surface Gravity Waves: Resonance in a Fish Tank", The= Physics Teacher 48 (2010) 330-332. Reference 3 of that paper is the book "= Hydrodynamics" by Sir Horace Lamb, 6th ed. (1932). In Chapter IX of that te= xtbook, "Surface Waves", standing surface gravity waves in a horizontal she= et of water are discussed in detail. Eq. (11) [page 365] gives the liquid-p= article displacements versus time and place for arbitrary water-sheet thick= ness, and in a diagram on page 366, the streamlines are shown for sheet thi= ckness much greater than the&nbsp;wavelength. In the text below that diagra= m, it is mentioned that these waves occur in troughs if their vertical wall= s coincide with antinodes (where the liquid particles oscillate vertically)= .</FONT></P> <P><FONT size=3D2>Reinhart.&nbsp; <BR><BR>Reinhart Frosch,<BR>Dr. phil. nat= .,<BR>CH-5200 Brugg.<BR>reinifrosch@xxxxxxxx .</FONT> </P></div></body></= html> ------=_Part_2985_24757556.1303915104534--


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