A wire stretched between two rigid supports vibraes in its fundamental mode with a frequency of45 Hz. The mass of the wire is `3.5 xx 10^(-2) kg` and its linear mass density is`4.0 xx 10^(-2) kgm^(-1)`. What is (a) the speed of transverse wave on the string and ( b) the tension in the string ?

Explanation

Given,` f = 45 Hz, mu = 4.0xx 10^(-2) kgm^(-1) , M =3.5 xx 10^(-2) kg, v = ? ` , Tension T=?
By definition, linear density `mu = ( M )/( L)`
hence length of the string `L = (3.5 xx 10^(-2))/( 4.0 xx 10^(-2))`
i.e., L = 0.875m
We know that, `f = ( 1)/(2L) sqrt((T)/(mu))`
i.e., `T = 4L^(2) f^(2) mu =4 xx 0.875 xx 0.875 xx( 45)^(2) xx 4 xx 10^(-2) `
`T = 248.0N`
Speed of a transverse wave on the string ,
`v = sqrt((T)/( mu ))`
i.e., `v = sqrt((248 )/( 4 xx 10^(-2))) = 78.74 ms^(-1)`