A stretched string fixed at each end has a mass of $50\mathrm{.}0$ g and a length of $8\mathrm{.}60$ m $.$ The tension in the string is $41\mathrm{.}0$ 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.$)$

nodes:

smallest distance $$ m

$$ m

largest distance $m$

antinodest

smallest distance $$ m

$$ m

largest distance $$ Im

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

$$ Hz