A set of 12 tuning forks is arranged in order of increasing frequencies. Each fork produces Y beats per second with the previous one. The last is an octave of the first. The fifth fork has frequency of 90 Hz. Find Y and the frequency of the first and the last tuning forks.

A set of 12 tuning forks is arranged in order of increasing frequencie

1.	A set of 12 tuning forks is arranged in order of increasing frequencies. Each fork produces Y beats per second with the previous one. The last is an octave of the first. The fifth fork has frequency of 90 Hz. Find Y and the frequency of the first and the last tuning forks.
Answer» Solution :Data ` n_(i+1) - n_(1) =Y., n_(12) = 2n_(1) , n_(5) = 90Hz` ` n_(2) -n_(1)` Y beats/s `"" n_(2)= n_(1) + ` Y beats/ s Siimilarly `n_(3) = n_(2) + Y= n_(1) + Y +Y` `n_(3) =n_(1) +2Y =n_(1) + (3-1) Y` ` n_(x) =n_(1) + (x-1) Y` SIMILARLY` n_(12) = n_(1) + (12-1) Y= n_(1) +11Y` `n_(12) -2n_(1)= n_(1) + 11Y` Also ` n_(5) = n_(1) + (5-1) Y = n_(1) + 4 Y` ` n_(5) = 11Y + 4 Y = 15 Y ` `n_(5) = 90 Hz ` Y =6 The frequency of the FIRST FORK ` n_(1) = 11Y ` beats/s= `11 xx 6 "beats/s " 66 Hz` and the frequency of the last fork ` n_(12) =2n_(1) = 2(66) =132` Hz

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A set of 12 tuning forks is arranged in order of increasing frequencies. Each fork produces Y beats per second with the previous one. The last is an octave of the first. The fifth fork has frequency of 90 Hz. Find Y and the frequency of the first and the last tuning forks.

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