Question

The tension in vibrating streched piano wire is 10 N. To double the frequency, the tension in wire must be

• A. 5 N
• B. 20 N
• C. 40 N
• D. 80 N

Answer 1

Answer: (C)

40 N

Answer 2

The fundamental frequency (n) of a wire of length I and tension T is given by $n=\frac{1}{2l}\sqrt{\frac{T}{m}},$ where m is mass per unit length of wire. Given, ${{n}_{1}}=n,{{T}_{1}}=T,{{n}_{2}}=2n$ $\therefore$ $\frac{{{n}_{1}}}{{{n}_{2}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}$ ${{T}_{2}}={{\left( \frac{{{n}_{2}}}{{{n}_{1}}} \right)}^{2}}{{T}_{1}}$ $\therefore$ ${{T}_{2}}={{(2)}^{2}}\times 10=40N$