Two strings \(\mathrm{A}\) and \(\mathrm{B}\) produce beat of frequency \(\Delta f_1>0\). The tension in string \(\mathrm{A}\) is slightly increased and the beat frequency is found to be \(\Delta f_2>0\). If the original frequency of \(\mathrm{A}\) is \(f_0\) and \(\Delta f_2 < \Delta f_1\), then the frequency of \(\mathrm{B}\) is

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.