Question

If vibration of string is 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 $T_{1}=T$
Vibration 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 $T_{2}=4 T_{1}$