Physics: Principles and Problems

Chapter 15: Sound

Problem of the Week

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Champ
"20-foot serpent thick as a barrel and a head like a horse" claims Samuel de Champlain and thus, July 1609 marked the first recorded sighting of the monster of Lake Champlain, aka Champ. Since that time, hundreds of sightings have been cataloged. Some suggest the beast is a surviving prehistoric plesiosaur, others are more skeptical.
Well, you see, it's just the water sloshing.

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Seiche
Scientist refer to a water slosh as a seiche [sigh shh] except if it is really big, then it is called a tsunami. A seichi is simply a standing wave in water, similar to the standing wave in air inside musical instruments.

To model the seiche of Lake Champlain, simplify the lake into two layers, the warm top layer and the cold bottom layer. Prevailing winds push top-layer water up the lake. When the wind stops, the excess water will slosh back and forth at the resonant frequency of the lake. The first-order frequency equation for a closed lake is:
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0078458137/193800/ch15_freq.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>, where g is the acceleration of gravity, h is the depth of the waving layer, and L is the length of the lake.

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The Plesiosaur was last seen
65 million years ago —maybe.
Model of Lake Champlain
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0078458137/193800/arrowLeft.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>    60 miles long    <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0078458137/193800/arrowRight.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0078458137/193800/arrowLeft.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a> prevailing wind
Epilimnion— warm, top layer;
extends down 65 feet
Hypolimnion— cold, dense water;
up to 400 feet deep
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0078458137/193800/POWproblem1.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a> Calculate the speed of some log or other debris that happens to 'catch a ride' on a seiche down the length of the lake. Assume the seiche only occurs in the top layer. Suppose the log rode the wave the whole length of the lake, how long would it take?
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0078458137/193800/webLinks.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> For an excellent demonstration of seicheing,
look at the Seiche Calculator at http://www.coastal.udel.edu/faculty/rad/
seiche.html
. Clicking will launch a new window.
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