Question

A wire having a linear mass density of `5.0xx10^(-3)kgm^(-1)` is stretched between two rigid supports with a tension of 45N. The wire resonates at a frequency of 420Hz. The next higher frequency at which the wire resonates is 490Hz. Find the length of the wire.

Answer 1

Suppose the wire vibratees at a frequency of 420 Hz is nth harmonic and at a frequency of 490 Hz in `(n+10)` the harmonic.
As, `v=(n)/(2l)sqrt((T)/(m)):. 420=(n)/(2l)sqrt((T)/(m))` …(i)
`490=(n+1)sqrt((T)/(m))`
`:. (490)/(420)=(n+1)/(n) :. n=6`
From (i) , `420=(6)/(2l)sqrt((450)/(5xx10^(-3)))=(900)/(l)`
`l=(900)/(420)=2.1m`