Question

Two identical 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 still remains unchanged. Denoting by $T_{1}$ and $T_{2},$ the higher and the lower initial tensions in the strings, it could be said that while making the above changes in tension:

• A. $T_{1}$ was decreased
• B. $T_{1}$ was increased
• C. $T_{2}$ was increased
• D. $T_{2}$ was decreased

Answer 1

Answer: (A)

$T_{1}$ was decreased

Answer 2

The relation for frequency and tension is given by $f \propto \sqrt{T}$ As $T_{1}>T_{2}$ i.e., $f_{1}>f_{2}$ So, $f_{1}-f_{2}=6\, Hz$ when we increase lower tension $T_{2}$, then $f_{2}$ will be increased and $f_{1}$ will decrease Hence, $f_{2}-f_{1}=6\, Hz$