Nine tuning forks are arranged in order of increasing frequency. Each tuning fork produces 4 beats per second when sounded with either of its neighbours. If the frequency of the `9^(th)` tunning fork is twice that of the first, what is the frequency of the first tuning fork ?

Options

A. 32 Hz
B. 40 Hz
C. 48 Hz
D. 56 Hz

Answer

A

Explanation

`n_(2) - n_(1) = 4 " " :. n_(2) = n_(1) + 4`
`n_(3) = n_(1) + 4 xx 2`
`n_(9) = n_(1) + 4 xx 8 " as " n_(9) = 2n_(1)`
`:. 2n_(1) - n_(1) = 32`
`:. n_(1) = 32 Hz`