A wire stretched betweentwo right supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is `3.5 xx10^(-2) kg ` and its linear mass density is `4.0 xx10^(-2) kg m^(-1)`. What is (a) the speed of transverse wave on thestring . and (b) the tension in the string ?

Explanation

Here, `v =45 Hz, mu = 3.5 xx 10^(-2) kg `
Mass `//` length `=mu =4.0 xx 10^(-2) kg //m`
`l =(mu)/( mu )=(3.5 xx 10^(-2))/(4.0 xx 10^(-2)) = ( 7)/(8) `
As ` ( lambda)/( 2) = l = ( 7)/( 8) ` `:. lambda= ( 7)/(4)m =1.75 m `
(a) Thespeed of transverse wave
` v = v lambda= 45 xx 1.75 =78.75 m //s`
(b) As `v =sqrt((T)/(mu))`
`:. T= v^(2) xxmu = ( 78.75)^(2) xx4.0 xx 10^(-2)`
`=248 .06 N `