Two identical straight wires are stretched so as to produce $6$ beats per second when vibrating simultaneously. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by ${T_1},{T_2}$ the higher and the lower initial tensions in the strings $\left( {{T_1} > {T_2}} \right)$ , then it could be said that while making the above changes in tension
A. ${T_1}$ was decreased or ${T_2}$ was increased
B. ${T_1}$ was increased or ${T_2}$ decreased
C. ${T_1}$ was decreased or ${T_2}$ decreased
D. ${T_1}$ was increased or ${T_2}$ increased

Hint: In such cases when the problem is based on wave phenomena, we know that frequency of the waves directly varies with tension in the string, hence analyze every option with the scientific approach and check which option seems to be more appropriate for the given situation. Then, present the answer with a proper explanation.

Complete step by step solution:
Beat Frequency $f' = {f_1} - {f_2} = 6Hz$........(given)
As we know, the frequency is directly proportional to the velocity and the velocity is directly proportional to the tension in the string.
Since, ${T_1} > {T_2}$...........(given)
$\Rightarrow {v_1} > {v_2}$
And, ${f_1} > {f_2}$

Now, let us consider the 4 cases as:

Hence, the correct option is A.

Note: Since this is a problem of multiple-choice questions (theory-based) hence, it is essential that given conditions be analyzed very carefully to give a precise explanation. While writing an explanation of this kind of conceptual problem, always keep in mind to provide the exact reasons in support of your explanation.