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Question: In order to double the frequency of the fundamental note emitted by a stretched string, the length i...

In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to 34\frac{3}{4}th of the original length and the tension is changed. The factor by which the tension is to be changed, is

A

38\frac{3}{8}

B

23\frac{2}{3}

C

89\frac{8}{9}

D

94\frac{9}{4}

Answer

94\frac{9}{4}

Explanation

Solution

n=12lTm⇒n∝Tln = \frac{1}{2l}\sqrt{\frac{T}{m}} \Rightarrow n \propto \frac{\sqrt{T}}{l}

⇒ T2T1=(n2n1)2(l2l1)2=(2)2(34)2=94\frac{T_{2}}{T_{1}} = \left( \frac{n_{2}}{n_{1}} \right)^{2}\left( \frac{l_{2}}{l_{1}} \right)^{2} = (2)^{2}\left( \frac{3}{4} \right)^{2} = \frac{9}{4}