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Two tuning forks A and B, when vibrated ...

Two tuning forks A and B, when vibrated simultaneously, produce 5 beats per second. The forks produce resonances respectively with 36 cm and 37 cm long air columns of a tube closed at one end. What are the frequencies of the tuning forks ?

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If V is the velocity of sound in air , the fundamental frequency of a tube of length l closed at one end , is
` n = (V)/(4l)`
` :. N_(A) = (V)/(4 xx 36) , n_(B) = (V)/(4 xx 37)`
So, ` (n_(A))/(n_(B)) = (37)/(36) , ` clearly , ` n_(A) gt n_(B)` .
As 5 beats are produced per second , we have
` n_(A) - n_(B) = 5 `
or , `(n_(A))/(n_(B)) - 1 = (5)/(n_(B)) ` or , ` (37)/(36) - 1 = (5)/(n_(B)` or , ` (1)/(36) = (5)/(n_(B))`
or, ` n_(B) = 180 Hz`
` :. n_(A) = n_(B) + 5 = 180 + 5 = 185 ` Hz .
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