Two unifrom strectched strings A and B, made of steel, are vibrating under the same tension. If the first overtone of A is equal to the second overtone of B and if the radius of A is twice that of B, the ratio of the lengths of the strings is

Options

A. `2:3`
B. `1:2`
C. `1:3`
D. `1:4`

Answer

C

Explanation

Given , `1st` overtone of `A=2nd` overtone of `B`
`implies(1)/(l_(1))sqrt((T)/(pir_(1)^(2)d))=(3)/(2l_(2))sqrt((T)/(pir_(2)^(2)d))implies(r_(2))/(r_(1))=(3)/(2)((l_(1))/(l_(2)))`