stretched string fixed at each end has a mass of $30\mathrm{.}0$ g and a length of $7\mathrm{.}20$ m$.$ The tension in the string is $40\mathrm{.}0$ 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 mlargest distance m

antinodes:smallest distance m mlargest distance m

$($b$)$

What is the vibration frequency for this harmonic?

Hz