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

Options

A. `9:01`
B. `1:09`
C. `3:01`
D. `1:03`

Answer

a

Explanation

`v = 1/(2l)sqrt(T/m) rArr v prop sqrt(T)/l`
`T_(2)/T_(1)=[v_(2)/v_(1)]^(2)[l_(2)/l_(1)]^(2)=[300/200]^(2)[(2l)/l]^(2)=9/1`