Determing in what way and how many times will the fundamental tone frequency of a stretched wire change it its length is shortened by `35 %` and the tension increased by `70%`.

Explanation

Let initial length and tension be `l` and `T` respectively.
So, `v_(1)=(1)/(2L) sqrt((T)/( rho_(1)))`
In accordance with the problem , the new length
`l^(')=l-(lxx35)/(100)=0.65l`
and new tension, `T^(')=T+(Txx70)/( 100)= 1.7 T`
Thus the new frequency
`v_(2)=(1)/(2l^('))sqrt((T^('))/(rho_(1)))=(1)/( 2 xx0.65l)sqrt((1.7T)/( rho_(1)))`
Hence `(v_(2))/( v_(1))=(sqrt(1.7))/( 0.65)=(1.3)/( 0.65)=2`