Each end of a string with

$=2\mathrm{.}10$ g$/$m

is attached to two opposite walls. The distance between the walls is

$34$

the length of the string. A block of mass m hangs from the middle of the string. Neglect the mass of the string in calculating the tension.

A block of mass m is suspended in midair. It is attached to the lower end of a short vertical string, and the upper end is attached to two long strings directed up and away from the short vertical string. Each long string makes the same angle with the horizontal. One long string points up and to the left of the vertical string to reach a vertical wall on the left, and the other long string points up and to the right of the vertical string to reach a vertical wall on the right. The long strings have length L $2$ and the walls are a distance $3$ L $4$ apart.

$($a$)$

Find an expression for the transverse wave speed in the string as a function of the mass of the block. $($Use the following as necessary: m$.$ Do not include units in your answer. Assume that m is measured in kg and v is measured in m$/$s$.)$

v $=$

$($b$)$

What is the mass of the block $($in kg$)$ if the wave speed is $44\mathrm{.}0$ m$/$s$?$