A string of mass M and length L hangs freely | vedclass

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(A) Let $T$ be the tension at a point at a distance $x$ from the free end.The mass of the string segment of length $x$ is $m_x = \frac{M}{L} x$.The te

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$\sqrt{gx}$

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(A) Let $T$ be the tension at a point at a distance $x$ from the free end.The mass of the string segment of length $x$ is $m_x = \frac{M}{L} x$.The tension $T$ at this point is equal to the weight of the string segment below it:$T = m_x \cdot g = \frac{M}{L} x g$.The linear mass density of the string is $\mu = \frac{M}{L}$.The velocity of a transverse wave on a string is given by $v = \sqrt{\frac{T}{\mu}}$.Substituting the values of $T$ and $\mu$:$v = \sqrt{\frac{(M/L) x g}{M/L}} = \sqrt{gx}$.

$A$ string of mass $M$ and length $L$ hangs freely from a fixed point. The velocity of a transverse wave along the string at a distance $x$ from the free end will be:

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