A wire of density 9 times 10^{-3} ,kg, cm ^{- | vedclass

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Question

$ho_{	ext {wire }}=9 	imes 10^{-3} \frac{ kg }{ cm ^{3}}=\frac{9 	imes 10^{-3}}{10^{-6}} kg / m ^{3}$

$=9000 kg / m ^{2}$

$( A = CSA$ of wi

Vedclass · Accepted Answer

$35$

Vedclass · Answer

$ho_{	ext {wire }}=9 	imes 10^{-3} \frac{ kg }{ cm ^{3}}=\frac{9 	imes 10^{-3}}{10^{-6}} kg / m ^{3}$

$=9000 kg / m ^{2}$

$( A = CSA$ of wire $)$

$\left( Y =9 	imes 10^{10} Nm ^{2}ight)$

$\left(ight.$ Strain $\left.=4.9 	imes 10^{-4}ight)$

$\Rightarrow L =1 m =\frac{\lambda}{2} \Rightarrow \lambda=2 m$

$\Rightarrow v=f \lambda \Rightarrow \sqrt{\frac{T}{\mu}}=f \lambda$

Where $Y=\frac{T / A}{	ext { strain }} \Rightarrow T=Y . A .$ strain

$\Rightarrow \sqrt{\frac{ Y . A . strain }{ m / L }}= f 	imes 2 \Rightarrow \sqrt{\frac{ Y . A I . 	ext { strain }}{ M }}= f 	imes 2$

$\Rightarrow \sqrt{\frac{ Y 	imes V 	imes 	ext { strain }}{ M }}= f 	imes 2 \Rightarrow \sqrt{\frac{ Y 	imes 	ext { strain }}{ho}}= f 	imes 2$

$f =\frac{1}{2} \sqrt{\frac{ Y 	imes 	ext { strain }}{ho}}=\frac{1}{2} \sqrt{\frac{9 	imes 10^{10} 	imes 4.9 	imes 10^{-4}}{9000}}$

$f=\frac{1}{2} \sqrt{\frac{9 	imes 10^{3}}{9} 	imes 4.9}=\frac{1}{2} \sqrt{4900}=\frac{70}{2}=35 Hz$

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