25 tuning forks are arranged in series in the order of decreasing frequency. Any two successive forks produce 3 beats/sec. If the frequency of the first turning fork is the octave of the last fork, then the frequency of the 21st fork is

Options

A. `72Hz`
B. `288Hz`
C. `84Hz`
D. `87Hz`

Answer

C

Explanation

`n_(max)-n_(min)=(N-1)Deltan` and `n_(max)=2n_(min)`
`implies2n_(min)-n_(min)=(24)xx3impliesn_(min)=72Hz`
The frequency of pth force is
`n_(p)=(p-1)Deltan+n_(min)`
The `21st` fork from max frequency is `5th` fork from minimum frequency
`:.n_(5)=4xx3+72=84Hz`