Answer
The tension in the string is $~~45.3~N$
Work Step by Step
We can find the difference in the resonant frequencies:
$\Delta f = 1320~Hz-880~Hz = 440~Hz$
Then $880~Hz$ is the second harmonic and $1320~Hz$ is the third harmonic, while the fundamental frequency of the string is $440~Hz$
We can find the wave speed along the string:
$f = \frac{nv}{2L}$
$v = \frac{2Lf}{n}$
$v = \frac{(2)(0.300~m)(440~Hz)}{1}$
$v = 264~m/s$
We can find the tension:
$v = \sqrt{\frac{\tau}{\mu}}$
$v^2 = \frac{\tau}{\mu}$
$\tau = \mu~v^2$
$\tau = (0.650\times 10^{-3}~kg/m)(264~m/s)^2$
$\tau = 45.3~N$
The tension in the string is $~~45.3~N$
