Answer
$k = 3.1~m^{-1}$
Work Step by Step
We can write a general expression for the standing wave:
$y'(x,t) = [(2y_m) sin ~(kx)]~cos~\omega t$
The standing wave has three loops on a string length of $3.0~m$
We can find the wavelength:
$\lambda = \frac{2L}{3}$
$\lambda = \frac{(2)(3.0~m)}{3}$
$\lambda = 2.0~m$
We can find $k$:
$k = \frac{2\pi}{\lambda}$
$k = \frac{2\pi}{2.0~m}$
$k = 3.1~m^{-1}$
