A string vibrates with a frequency 200Hz. Its length is doubled and its tension is altered until it begin to vibrate with frequency 300Hz. What is the ratio of the new tension to the original tension?

Explanation

The fundamental frequency of the string `n=1/(2l) sqrt((T)/mu)`
When the tension is `T_(1)`, the frequency is 200 Hz
`200=1/(2l) sqrt(T_(1)/mu) …….(i)`
When the length is 2l and the tension is `T_2`, the frequency is 300Hz
`300 =1/(2 xx 2l) sqrt(T_2/mu) ........(ii)`
Dividing equation (ii) by (i)
`(300)/(200), =(2l)/(4l) sqrt(T_2/T_1)`
`T_2/T_1=9/4 xx (16)/4 =9`
`T_2: T_1=9:1`