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. `1:2`
B. `1:3`
C. `1:4`
D. `1:5`

Answer

B

Explanation

Fundamental frequency of string
`n=1/(2l)sqrt(t/m`
Number of overtone = number of harmonic +1
`:. 2n_A=3n_B`
Since `r_A=2r_B`
Mass per unit length of string, `m=pir^2rho`
`n=1/(2l)sqrt(T/(mr^2rho))`
`n_A/n_B=l_B/l_Asqrt(r_B^2/r_A^2)`
`3/2=l_B/l_Axxr_B/(2r_B)`
`l_A/l_B=1/3`
`l_A:l_B=1:3`