Question

If vibration of string are to be two times, then tension in the string must be made:

• A. eight times
• B. four times
• C. twice
• D. half

Answer 1

Answer: (B)

four times

Answer 2

Here : initial vibration $n_{1}=n$, final vibration $n_{2}=2 n$ Initial tension $T_{1}=T$ Vibriation of frequency of string $n=\frac{1}{2 l} \sqrt{\frac{T}{m}}$ $\Rightarrow n \propto \sqrt{T}$ Hence, $\frac{n_{1}}{n_{2}} =\sqrt{\frac{T_{1}}{T_{2}}}$ or $\frac{T_{1}}{T_{2}} =\left(\frac{n_{1}}{n_{2}}\right)^{2}$ $=\left(\frac{n}{2 n}\right)^{2}=\frac{1}{2}$ or $T_{2} =4 T_{1}'$