Answer
$\mu = 0.45~g/m$
Work Step by Step
We can find the wave speed in the string:
$v = \lambda~f$
$v = 2L~f$
$v = (2)(0.65~m)(329.63~Hz)$
$v = 428.5~m/s$
We can find the mass per unit length of the string:
$v = \sqrt{\frac{F}{\mu}}$
$v^2 = \frac{F}{\mu}$
$\mu = \frac{F}{v^2}$
$\mu = \frac{82~N}{(428.5~m/s)^2}$
$\mu = 4.5\times 10^{-4}~kg/m$
$\mu = 0.45~g/m$
