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I have been told that trasverse wave propogates by the oscillation of medium particles in direction perpendicular to propogation.

Consider a wave on a taught string (x-y plane). What is the mechanism of movement of the same sinosudial function along the string?

Suppose we start moving the particle on one end sinosudialy the how come the next particle also moves sinosudialy? How does elastic force between them does this work? If we displace the particle, there is some elastic force developed which is at some angle with horizontal so the next particle should move at some angle and its vertical displacement should be less than the previous one.

So how come in a propogating wave all particle rise to the same height?

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The solution to the transverse string vibrations has been solved both mathematically and physically by Bernoulli, Euler and Fourier.

The basic method is to use the classical Newton's laws to assume the elastic forces between adjacent particles to be creating an infinitesimal tension between them, indirectly leading to an unbalanced upward force. This is what leads to the acceleration and the so-called wave equation. The wave equation is solved by the familiar processes of variable separation and fourier series.

The assumptions we make for the above derivation are that there are no non-newtonian forces and that the amplitude of oscillation is very small. Under these considerations, we see that the mathematical solution does produce waves of equal height.

Ref: http://www.math.ubc.ca/~feldman/apps/wave.pdf

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  • $\begingroup$ Sir , my question was that how is the same equationof SHM transferred along the string what mechanism causes the same diplacement of neighbour particles as the previous one ? $\endgroup$ – user28804 Dec 28 '13 at 3:06
  • $\begingroup$ Hi! The tension between adjacent particles(which is needed to keep the string intact) is what gives them the same type of motion. Go through the derivation again, feel free to ask! $\endgroup$ – Torsten Hĕrculĕ Cärlemän Dec 28 '13 at 18:14

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