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

First overtone of A = Second overtone of B
`l/l_1sqrt(T/(pir_1^2d))=3/(2l_2)sqrt(T/(pir_2^2d)`
`r_2/r_1=3/2(l_1/l_2)`
`r_2/(2r_2)=3/2(l_1/l_2)` `[:'r_1=2r_2]`
`1/2=3/2(l_1/l_2)`
`:. l_1:l_2=1:3`