Answer
The fundamental frequency of oscillation is $10~Hz$.
Work Step by Step
Let $L$ be the length of the string. The wave travels a distance of $L$ in a time of $0.050~s$. Therefore, the wave could travel a distance of $2L$ in a time of $0.10~s$, so this time is the period of the fundamental.
We can find the fundamental frequency:
$f = \frac{1}{T}$
$f = \frac{1}{0.10~s}$
$f = 10~Hz$
The fundamental frequency of oscillation is $10~Hz$.
