The fundamental frequency of a stretched string is given by $f = \frac{v}{2L}$. Since the tension and linear mass density of the string remain constant, the wave speed $v$ is constant. Therefore, the fundamental frequency is inversely proportional to the vibrating length of the string ($f \propto \frac{1}{L}$). We can write the relation as: $f_1 L_1 = f_2 L_2$. Given: Initial frequency, $f_1 = 120\text{ Hz}$ Initial length, $L_1 = 90\text{ cm}$ Final frequency, $f_2 = 180\text{ Hz}$ Let the new length be $L_2$. Substituting the values: $120 \times 90 = 180 \times L_2$ $L_2 = \frac{120 \times 90}{180} = 60\text{ cm}$. Therefore, the string should be pressed such that the vibrating length becomes $60\text{ cm}$.