A string of length \(L\) fixed at both ends is driven by a mechanical vibrator operating at a constant frequency \(f\). Under an initial string tension \(T_1\), a standing wave with four antinodes is established, as shown in the diagram. The tension is then gradually altered to a new value \(T_2\) without changing the frequency \(f\) or length \(L\), causing the string to shift into a standing wave pattern with two antinodes. The wave speed on a string of linear mass density \(\mu\) under tension \(T\) is given by \(v = \sqrt{\dfrac{T}{\mu}}\). What is the ratio \(\dfrac{T_2}{T_1}\) of the new tension to the initial tension?