First slide

Stationary waves

Question

The tension of a stretched string is increased by 69%. In order to keep its frequency of vibration constant, its length must be increased by

Moderate

A

20%
B

30%
C

$\sqrt{69} %$
D

69%

Solution

$n \propto \frac{\sqrt{T}}{l} \Rightarrow l \propto \sqrt{T}$ (As n = constant)
$\Rightarrow \frac{l_{2}}{l_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} = l_{1} \sqrt{\frac{169}{100}} \Rightarrow l_{2} = 1 .3 l_{1} = l_{1} + 30 % of l_{1}$

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