b
(b) Using \(n = \frac{1}{{2l}}\sqrt {\frac{T}{m}} \);

As \({T_1} > {T_2}\)==> \({n_1} > {n_2}\) giving \({n_1} - {n_2} = 6\)

The beat frequency of \(6\) will remain fixed when

\((i)\) \({n_1}\) remains same but \({n_2}\) is increased to a new value \(({n_2}^\prime - {n_2} = 12)\) by increasing tension \({T_2}\).

\((ii)\) \({n_2}\) remains same but \({n_1}\) is decreased to a new value \(({n_1} - {n_1}' = 12)\) by decreasing tension \({T_1}\).