A guitar string of length \(L_0\) and linear mass density \(\mu\) is fixed at both ends under tension \(T_0\). When plucked, the string vibrates in its fundamental standing wave mode with frequency \(f_0\). A musician presses down on a fret to reduce the active vibrating length of the string to \(L = \dfrac{3}{4}L_0\), and simultaneously adjusts the tuning peg so that the string tension increases to \(T = \dfrac{16}{9}T_0\). What is the ratio \(\dfrac{f}{f_0}\) of the new fundamental frequency to the original fundamental frequency?