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

Explanation

Here,`v=45Hz, M=3.5xx10^(-2)kg,` mass`//` length `=m=4.0xx10^(-2)kgm^(-1)`
`:. l=(M)/(m)=(3.5xx10^(-2))/(4.0xx10^(-2))=(7)/(8)m`
As, `(lambda)/(2)=l=(7)/(8) :. lambda=(7)/(4)m =1.75m. `
The speed of the transverse wave `upsilon=vlambda=45xx1.75=78.75m//s`
(b) As, `upsilon=sqrt((T)/(m)):. T=upsilon^(2)xxm=(78.75)^(2)xx4.0xx10^(-2)=248.06N`.