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  4. 25 tuning forks are arranged in series in the order of decreasing frequency. Any two successive forks produce 3 beats/s. If the frequency of the first tuning fork is the octave of the last fork, then the frequency of the 21st fork is:

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

KEAMKEAM 2001

Solution:

If n is the frequency of last fork then frequency of first fork be $ 2n $ .
So, $ 2n-(25-1)\times 3=n $
$ \Rightarrow $ $ n=72\,Hz $
21st fork frequency
$ =144-(21-1)(3) $
$ =84\text{ }Hz $