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  • A sitar wire is replaced by another wire of same length and material but of three times earlier radius. If the tension in the wire remains the same, by what factor will the frequency change?

A sitar wire is replaced by another wire of same length and material but of three times earlier radius. If the tension in the wire remains the same, by what factor will the frequency change?

Answers (1)

Frequency of wire stretched at both ends v=\frac{n}{2L}\sqrt{\frac{T}{m}}  

As the number of harmonics, length L and tension T is kept the same in both cases v\propto \frac{1}{\sqrt{m}} 

v_{1}/v_{2}=\sqrt{\frac{m_{2}}{m_{1} }}

 mass per unit length=mass of wire/length=\frac{\pi r^{2}l\rho}{l} = (\pi r^{2})\rho

As the material of wire is same

\frac{m_{2}}{m_{1}}=\frac{(\pi r^{2}_{2})\rho}{(\pi r_{1}^{2})\rho} =\frac{9}{1}   

\frac{v_{1}}{v_{2}}=\sqrt{\frac{9}{1}} =3

 

Posted by

infoexpert24

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