Two uniform strings, A and B made of steel are made to vibrate under the same tension. Radius of A is two times the radius of B . If the first overtone of A is equal to the second overtone of B, the ratio of lengths of the string is

Given that first overtone of string A is equal to second overtone of string 8. Thus the second harmonic of A is equal to third harmonic of B, i.e.,   or 21LArATπρ=31LBrBTπρ or 21LArATρ=31LBrBTρ or 2LArA=3LBrB or LALB=2rB3rA=2rB32rB or LALB=13  or  LA:LB=1:3