16 tuning forks are arranged in the order of decreasing frequency. Any two successive forks gives 5 beats per second when sounded together. If the first tuning fork gives the octave of the last, then determine the frequency of the last fork.

Explanation

No. of tuning forks = 16
No. of beats = 8
`" "` [between two successive forks]
Suppose frequency of first fork = 2n
`" "` frequency of last fork = n
Frequencies in the given arrangement are as follows :
`" "n_(2)=2n`
`" "n_(2)=2n-1 times 8`
`" "n_(3)=2n-2 times 8`
`" "n_(4)=2n-3 times 8`
`" "n_(16)=2n-15 times 8`
Frequencies of last fork = n
`" "2n-150 = n`
`" "n =120`
So, frequency of last fork = 120 Hz.