Two strings have lengths in the ratio `2:3` ,radii in the ratio `3:4` .They are tensioned in the ratio `16:25` .If they are made of the same material,the ratio of the frequencies emitted by them in the fundamental mode is

Explanation

Data ` : L_(1) = 30 cm , L_(2) = 40 cm , r_(1) /r_(2) = 4/5 , rho_(1)/rho_(2) = 6/5, T_(1) /T_(2) = 3/4`
Fundamental frequency n` = 1/(2L) = sqrt(T/m) = 1/(2L) sqrt(T/(pir^(2)P)) = 1/(2Lr) sqrt(T/(rrho))`
` n_(1)/n_(2) = (L_(2))/L_(1) r_(2)/r_(1) sqrt(T_(1)/T_(2) rho_(2)/rho_(1)) = 4/3xx 5/4 sqrt(3/4 xx 5/6) = 5/6 sqrt(5/2) = 1.317 `