A stretched string fixed at each end has a mass of $38\mathrm{.}0$ g and a length of $9\mathrm{.}00$ m$.$ The tension in the string is $46\mathrm{.}0$ 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 m largest distance m

antinodes: smallest distance m m largest distance m

$($b$)$

What is the vibration frequency for this harmonic?

Hz