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If vibration of string is to be two times, then tension in the string must be made
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Verified Answer
The correct answer is:
four times
Here: Initial vibration $n_1=n$, final vibration $n_2=2 n$
Initial tension $T_1=T$
Vibration of frequency of string
$n=\frac{1}{2 l} \sqrt{\frac{T}{m}}$
$\Rightarrow \quad n \propto \sqrt{T}$
Hence,
$\frac{n_1}{n_2}=\sqrt{\frac{T_1}{T_2}}$
or $\frac{T_1}{T_2}=\left(\frac{n_1}{n_2}\right)^2=\left(\frac{n}{2 n}\right)^2=\frac{1}{4}$
or $T_2=4 T_1$
Initial tension $T_1=T$
Vibration of frequency of string
$n=\frac{1}{2 l} \sqrt{\frac{T}{m}}$
$\Rightarrow \quad n \propto \sqrt{T}$
Hence,
$\frac{n_1}{n_2}=\sqrt{\frac{T_1}{T_2}}$
or $\frac{T_1}{T_2}=\left(\frac{n_1}{n_2}\right)^2=\left(\frac{n}{2 n}\right)^2=\frac{1}{4}$
or $T_2=4 T_1$
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