Problems for Edward F. Redish |
The displacement of a bit of a transversely oscillating string satisfies the wave equation
where
T is the tension of the string and ρ is the mass density (mass per unit length) of the string.
(a) For a string connected between two fixed points at x = 0 and x = L , find the frequencies and shapes of the normal modes of the system. (Be sure to show how you get these conclusions starting from the information given.)(b) Suppose at t ≤ 0, the string is held so that y(x,0) = f(x). At the time t = 0 the string is released. Explain how you would go about finding y ( x,t ) for t > 0 and write equations that would allow you to calculate that function if you had a computer available.
University of Maryland | Physics Department | Physics 374 Home |
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Last revision 2. December, 2005.