Answer
$K=141m^{-1}$
Work Step by Step
We can find the wave number through the formula:
$k=\frac{2\pi}{\lambda}$........eq(1)
Also, we know that; $\lambda=\frac{v}{f}$
Also, $v=\sqrt\frac{T}{\mu}$ where $T$ and $\mu$ represent tension in the string and linear mass density of the string respectively.
We then substitute this formula of $v$ in the formula of $\lambda$ to attain,
$\lambda=\frac{\sqrt\frac{T}{\mu}}{f}$
We plug this formula of $\lambda$ in eq(1) to obtain:
$K=2\pi f \sqrt\frac{\mu}{T}$
We plug in the known values to obtain:
$k=2(3.1416)\sqrt\frac{0.5}{10}=141m^{-1}$
