$11\mathrm{.}9-$kg object hangs in equilibrium from a string with a total length of

$5\mathrm{.}90$ m

and a linear mass density of

$=0\mathrm{.}00500$ kg$/$m$.$

The string is wrapped around two light frictionless pulleys that are separated by a distance of

d $=2\mathrm{.}00$ m$.$

Two figures show a system of two pulleys and a block of mass m attached to each other with string in a triangular arrangement. The pulleys are at the top left and top right of the triangle, separated by a distance d$.$ The block connects directly to the bottom corner of the triangle, pulled downward by gravity vector g$.$ In figure $($a$),$ the string connecting the pulleys is completely horizontal and unmoving. In figure $($b$),$ the string connecting the pulleys is oscillating as a standing wave such that there is one and a half wavelengths between the pulleys.

$($a$)$ Determine the tension in the string.

N

$($b$)$ At what frequency must the string between the pulleys vibrate in order to form the standing$-$wave pattern shown in Figure b$?$

Hz