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 490 Hz. Find the length of the wire.

Explanation

Suppose the wire vibrates at 420 Hz in its `n^(th)` harmonic and at 490 Hz in its `(n+1)^(th)` harmonic.
`(490)/(420)=(n+1)/(n)= or =6 rArr 420=(6)/(2l) sqrt((450)/(5.0xx10^(-3)))`
`:.l=(900)/(420)=2.1m`