Answer
See explanation.
Work Step by Step
The fundamental frequency is given by equation 15.35.
$$f_1=\frac{1}{2L}\sqrt{\frac{F}{\mu}}$$
By pressing the string in the middle, the violinist decreases the length L of the vibrating portion, by a factor of 2.
The fundamental frequency is multiplied by 2, i.e., the new note is one octave higher.