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![[Post New]](/templates/default/images/icon_minipost_new.gif) 5 Apr 2007 18:54:26 IST
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Demonstrate that any differentiable function f(t+ax), where a is a constant provides a solution of wave equation. what is the physical meaning of thwe constant a
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5 Apr 2007 19:45:48 IST
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Dear tejasvi... any function of the term (x +/- vt ) and containing no other term of x will be the equation of a wave.
Further, the wave will be practically possible if the function nevers attains infinite value for finite value of x and t, that means it should not be exponential etc. function..
The derivation is little abstrac.. let me try to explain the logic..
Wave is actually SHM of a large no. of continuous particles, with uniformly changing phase angel... now suppose the total phase of particle A at time x,t =0 be p. Then, as the wave travels at speed v, it would have traveled distance vt in time t. So, the same eqn. of SHM will be applicable for the particle B, situated at dist vt from A, if we replace the x term in the SHM eqn by x+vt or x-vt.... hence the result..
Also remember, if we have x-vt, the wave is traveling in the positive x dirn, and if we have x+vt, the wave is traveling in negative x direction (proof is similar to above...do try it yourself if you understand the first one)
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Sudeep Kumar
(B tech, IITd)
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this reply: 10 points
(with 2 
in 2 votes ) [?]
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