Two identical musical strings, 1 and 2, have the same length and linear mass density. String 1 is initially under tension \(T_1 = T_0\) and String 2 is under tension \(T_2 = 1.21 T_0\). When both strings vibrate simultaneously in their fundamental mode, a beat frequency of \(4.0\text{ Hz}\) is heard. The tension in String 1 is then increased to \(T_1' = 1.69 T_0\) while the tension in String 2 remains unchanged. What is the new beat frequency heard when both strings vibrate in their fundamental mode?