Two identical straight wires are stretched so as to produce $6$ beats per second when vibrating simultaneously. On changing the tension 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, then it could be said that while making the above change in tension
IIT 1991, Medium
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(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 ${T_1}$.
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