A string of length $L$ and mass $M$ hangs freely from a fixed point. Then the velocity of transverse waves along the string at a distance $x$ from the free end is
Diffcult
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(b) Velocity $v = \sqrt {\frac{T}{m}} $;
where $T = $ weight of part of rope hanging below the point under consideration
$ = \left( {\frac{M}{L}} \right)xg$
==> $v = \sqrt {\frac{{\left( {\frac{M}{L}} \right)xg}}{{\left( {\frac{M}{L}} \right)}}} = \sqrt {xg} $.
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