A string vibrates with a frequency of 200Hz . When its length is doubled and tension is altered , it begins to vibrate with a frequency of 300 Hz . The ratio of the new tension to the original tension is

Options

A. `3 : 1`
B. `1 : 3`
C. `9 : 1`
D. `1 : 9`

Answer

C

Explanation

`v_(1)=(1)/(2l_(1))sqrt((T_(1))/(mu))rArrT_(1)=v_(1)^(2)*4l_(1)^(2)*mu`
`T_(2)=v_(2)^(2)*4xx4l_(1)^(2)*mu. " "v_(1)=200Hz,v_(2)=300`.
`therefore(T_(2))/(T_(1))=(90000)/(40000)xx4rArr(T_(2))/(T_(1))=9:1`.