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A wire of density 9000 kg//m^(3) is stre...

A wire of density `9000 kg//m^(3)` is stretched between two clamps `100 cm` apart while subjected to an extension od `0.05 cm`. What is the lowest frequency of transverse vibrations in the wire , assuming Young's modulus of the material to be `9 xx 10^(10) N//m^(2)`?

Text Solution

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Here, `rho=9g//c c=9xx10^(3)kg//m^(3)`
`l=100cm=1m`
`Deltal=0.05cm=5xx10^(-4)m`
`v=?`
`Y=9xx10^(9)N//m^(2)`
From `Y=(F//A)/(Deltal//l)=(Tl)/(ADeltal)`
`(T)/(A)=Y(Deltal)/(l)=9xx10^(10)xx(5xx10^(-4))/(1)`
`=45xx10^(6)N//m^(2).`
Now, `v=(1)/(2l)sqrt((T)/(m))=(1)/(2l)sqrt((T)/(Arho))`
`=(1)/(2xx1)sqrt((45xx10^(6))/(9xx10^(3)))=(1)/(2)sqrt(5000)=35.4Hz`
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