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For one wire tied at both the ends with ...

For one wire tied at both the ends with a tension of 450 N, linear density of mass is 0.05 g/cm. It sounds resonantly for two consecutive frequencies 420 Hz and 490 Hz. Find length of this wire.

Text Solution

Verified by Experts

In the present case, frequency of `n^(th)` harmonic
`f _(n) = n f _(1) = 420 Hz`
`f _(n +1) = (n +1) f _(1)= 490 Hz `
Taking subtraction, `n f _(1) + f _(1) -nf _(1) = 490 -420`
`therefore f _(1) = 70 Hz`
`therefore (1)/(2L) sqrt ((T)/( mu )) =70`

`therefore L = (300)/(140) =2.1428 m ~~2.143 m`
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