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A piano wire weighing 6.00 g and having ...

A piano wire weighing 6.00 g and having a length of 90.0 cm emits a fundamental frequency corresponding to the "Middle C" (v = 261.63 Hz). Find the tension in the wire.

Text Solution

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The correct Answer is:
1480N
`l=90cm=0.9m`
`m=(6/90)gm/cm`
`={(6xx10^-3)/(90xx10^2)}kg/m`
`=(6/900)kg/m`
`f=261.63Hz`
`f=1/(2L)sqrt((T/m))`
`rarr `261.63= `1/((2xx0.09))sqrt{(Txx900)/6}`
`rarr 0.18x261.63=sqrt(150T)`
`rarr 150T=(261.63xx0.18)^2`
`rarr T=((261.63xx0.18)^2)/150`
`=1478.52N=1480N`
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