First slide

Beats

Question

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 T₁, T₂ , the higher and the lower initial tensions in the strings, then it could be said that while making the above change in tension

Moderate

A

T₂ was decreased
B

T₂ was increased
C

T₁ was increased
D

T₁ was kept constant

Solution

Using $n = \frac{1}{2 l} \sqrt{\frac{T}{m}}$ ;
As $T_{1} > T_{2} \Rightarrow n_{1} > n_{2}$ giving $n_{1} - n_{2} = 6$
The beat frequency of 6 will remain fixed when
(i) n₁ remains same but n₂ is increased to a new value $({n_{2}}^{'} - n_{2} = 12)$ by increasing tension T₂.
(ii) n₂ remains same but n₁ is decreased to a new value $(n_{1} - {n_{1}}^{'} = 12)$ by decreasing tension T₁.

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