A set of 28 turning forks is arranged in an increasing order of frequencies. Each fork produces ' x ' beats per second with the preceding fork and the last fork is an octave of the first. If the frequency of the 12^ th fork is 152 Hz , the value of ' x ' (no. of beats per second) is

Step-by-step solution

Forks arranged in a series of increasing frequency from n ₁ to n ₂₈ Each for produces ' x ' beats with preceding fork, For. 12^ th fork, n ₁₂= n ₁+11 x 152= n ₁+11 x Similarly, n ₂₈= n ₁+27 x Given condition is n ₂₈=2 n ₁2 n ₁= n ₁+27 x n ₁=27 x Substituting this value in equation (i), array ll & 152=27 x+11 x & x= 152 38 =4 array ...(i)