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(C) The speed of a transverse wave on a string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density of

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$\sqrt{\frac{g L}{2}}$

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(C) The speed of a transverse wave on a string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density of the string.For a hanging rope of length $L$ and linear mass density $\mu$,the tension $T$ at a distance $y$ from the lower end is due to the weight of the rope segment below it.The mass of the rope segment of length $y$ is $m = \mu y$.Thus,the tension at distance $y$ is $T = \mu y g$.The speed of the pulse at distance $y$ is $v = \sqrt{\frac{\mu y g}{\mu}} = \sqrt{gy}$.At the midpoint of the rope,$y = \frac{L}{2}$.Therefore,the speed of the pulse at the midpoint is $v = \sqrt{g \left(\frac{L}{2}\right)} = \sqrt{\frac{g L}{2}}$.

$A$ pulse is generated at the lower end of a hanging rope of uniform density and length $L$. The speed of the pulse when it reaches the midpoint of the rope is:

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