A weight of mass **M** is hanging from a string. The string has length \(\ell\); its mass **m** is uniformly distributed.

A small disturbance of the hanging mass **M** causes a transverse pulse wave to travel up the string. The time it takes for this pulse to reach the top of the string can be written as
\[t = c\sqrt{\frac{\ell}{g}},\]
where **c** is a dimensionless number. What is the correct expression for **c**?

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