In an experimental acoustics laboratory, a stationary wave is set up on a high-tension carbon-fiber monofilament (String A) of length $L_A$ and diameter $D_A$, under a tension $T_A$.

A second monofilament (String B) is made from the same carbon-fiber material but has a length $L_B=1.6L_A$ and is subjected to a tension $T_B=1.44T_A$.

Determine the ratio of the diameter of String B to String A, $\frac{D_B}{D_A}$, required for String B to vibrate with the same fundamental (first-harmonic) frequency as String A.