stretched string fixed at each end has a mass of $44\mathrm{.}0$ g and a length of $7\mathrm{.}00$ m$.$ The tension in

the string is $42\mathrm{.}0$ N$.$

$($a$)$ Determine the positions of the nodes and antinodes for the third harmonic. $($Enter your

answers from smallest to largest distance from one end of the string.$)$

$($b$)$ What is the vibration frequency for this harmonic?