A string is fixed at both ends. The tension in the string and density of the string are accurately known but the length and the radius of cross section of the string are known with some errorl If maximum errors made in the measurements of length and radius are `1%` and `0.5%` respectively them what is the maximum possible percentage error in the calculation of fundamental frequencyof the that string ?

Answer

`1.5%`

Explanation

`f=(1)/(2l)sqrt((T)/(mu))=(1)/(2l)sqrt((T)/(rhoS))=(1)/(2l)sqrt((T)/(rho.pir^(2)))=(1)/(2lr)sqrt((T)/(rho pi))`
`:. (Deltaf)/(f)=-(Deltal)/(l)-(Deltar)/(r)`
`((Deltaf)/(f))_(max)=1+0.5=1.5% Ans. `