Two idential 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 tension in the strings, then it could be said that while making the above changes in tension,

Options

A. (a) `T_(2)` was decreased
B. (b) `T_(2)` was increased
C. ( c ) `T_(1)` was decreased
D. (d) `T_(1)` was increased

Answer

B, C

Explanation

(b,c) As, `f = (1)/(2pi)sqrt((T)/(mu))` :. `f prop sqrt(T)`
Given that `T_(1) gt T_(2)` :. `f_(1) gt f_(2)`
Initially beat frequency `(f_(1) - f_(2)) = 6`.
The beat frequency remains unchanged which is possible when `f_(2)` increases and `f_(1)` decreases. thua `T_(2)` increases and `T_(1)` decreases.