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A wire having a linear mass density 5.0 ...

A wire having a linear mass density `5.0 xx 10^(-3)` kg/m is stretched between two rigid supports with a tension of 450 N. The wire resonates at a frequency of 420 Hz. The next higher frequency at which the same wire resonates is 480 Hz. Find the length of the wire.

Text Solution

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Suppose the wire vibrates of 420 Hz in its nth harmonic and at 490 Hz in its (n + 1) th harmonic.
`420 = (n)/(2L) sqrt((T)/(mu))" "...(i)`
and `490 = ((n + 1))/(2L) sqrt((T)/(mu))" "…(ii)`
Substracting equation (i) from (ii)
`(1)/(2L) sqrt((T)/(mu)) = 60`
`rArr L = (1)/(2 xx 60) sqrt((T)/(mu))`
`therefore L = (1)/(2xx 60) sqrt((450)/(5 xx 10^(-3))) = 2.5` m
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