A set of 25 tuning forks is arranged in order of decreasing frequency. Each fork gives 3 beats with succeeding one. The first fork is octave of the last. Calculate the frequency of the first and 16th fork.

Options

A. 144 Hz
B. 99 Hz
C. 95 Hz
D. 85 Hz

Answer

B

Explanation

`N = (n_(f) - n_(L))/(x) + 1`
`25 -1 = (2n_(L) - n_(L))/(3)`
`24 xx 3 = n_(L)`
`72 = n_(L)`
`n_(f) = 2n_(2) = 2 xx 72 = 144`
`n_(1) - n_(2) = 3`
`n_(1) = n_(2) + 3`
`n_(1) = n_(3) + 2 xx 3`
`n_(1) = n_(16) + 15 xx 3`
`n_(16) = 144 - 45 = 99Hz`