A wire under tension vibrates with a fundamental frequency of 600 Hz.If the length of the wire is doubled,the radius is halved and the wire is made to vibrate under one-ninth the tension.Then the fundamental frequency will become

Options

A. 200 Hz
B. 300 Hz
C. 600 Hz
D. 400 Hz

Answer

A

Explanation

`v = (1)/(2l) sqrt((T)/(m))`
`therefore 600 = (1)/(2l) sqrt((T)/(m)) `
v. = `(1)/(2l.) sqrt( (4 T.)/(rho pi D^(2).))`
` therefore v. = (1)/(2.2l) sqrt( (4 T//9)/(rho pi. (D^(2))/(4))) = (1)/(l) sqrt( ( T)/(9 rho pi D^(2))) = (1)/(3l) sqrt( (T)/(rho pi D^(2)))`
` therefore (v.)/(v) = (2l)/(3l) sqrt( ( T)/(rho pi. D^(2))) xx sqrt((rho pi D^(2))/(4T)) = (1)/(3) `
so correct choice is a.