A set of 14 tuning forks is arranged in a series of increasing frequencies. Each fork produces ' x ' beats per second with the preceding fork and the last fork is an octave of the first fork. If the seventh fork has the frequency of 114 Hz, the value of x is

Step-by-step solution

Let the frequency of the first tuning fork be f₁ . Since each fork produces x beats per second with the preceding fork and the frequencies are in increasing order, the frequencies form an arithmetic progression with a common difference of x . The frequency of the n -th tuning fork is given by f_n = f₁ + (n - 1)x . The frequency of the 14th tuning fork is f₁₄ = f₁ + 13x . It is given that the last fork is an octave of the first fork, which means f₁₄ = 2f₁ . Substituting this into the equation, we get 2f₁ = f₁ + 13x