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Re: [Phys-l] waves on a string



Looking over this development of the wave equation from Fowler, you notice near the foot in a para about energy, the handling of tension,
supposed constant, in the face of varying string extension.

http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/AnalyzingWaves.htm

Brian W

On 12/12/2010 7:41 PM, Al Bachman wrote:
/snip/"why does the energy at each point have to be constant ?" It seems to me that all that is required is constancy of the total energy summed over the string.
Second, even with small amplitude, the length of any section of string varies, therefor there should be additional forces along the length of the string causing the mass density of the string to vary. This violates the elementary assumption that the tension in the string is constant. There ought to be a longitudinal standing density wave as well as the transverse wave.
Is this another case of trying to determine too much from a first order approximation ?
Al Bachman