Two uniform stretched steel strings A and B are vibrating under the same tension. The first overtone of A is equal to the second overtone of B . If the radius of A is twice that of B , then the ratio of the lengths of the strings is

Step-by-step solution

Frequency in stretched string, f= n 2 l v= n 2 l T m where, l= length, T= tension and m= mass per unit length So, m= r^2 l d l , where, d= density and m= r^2 d . Given, f_A (first overtone, n=2 ) aligned & =f_B( second overtone, n=3) 2 2 l_A T m_A & = 3 2 l_B T m_B 1 l_A r_A^2 d = 3 2 l_B r_B^2 d l_A l_B & = 2 3 r_B r_A = 2 3 1 2 l_A l_B = 1 3 aligned