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24 tuning forks are arranged in the asce...

24 tuning forks are arranged in the ascending order of their frequencies. Each fork produces 4 beats per second with its immediately preceding fork . The last fork emits an octave to that emitted by the first one. Find out the frequencies of the first and the last tuning forks.

Text Solution

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Let the frequencies in ascending order of the 24 tuning forks be `n_(1) , n_(2) * * *, n_(24)` . The date for deat frequencies tells that
`{:(" "n_(2)-n_(1)=4),(" "n_(3)-n_(2)=4),(" ....................."),(" "n_(24)-n_(23) =4),(bar(("on addition")n_(24)-n(1)=23xx4=92)):}`
As the 24 th tuning fork emits an octave to that emitted by the first one , `n_(24) = 2n_(1)`
` :. 2n_(1) - n_(1) = 92 or , n_(1) = 92` Hz .
`:. n_(24) = 2n_(1) = 2 xx 92 = 184 ` Hz .
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