Two open organ pipes of fundamental frequencies `n_(1) and n_(2)` are joined in series. The fundamental frequency of the new pipes so obtained will be

Options

A. `n_(1) + n_(2) `
B. `(n_(1)^(2)+n_(2)^(2))/2 `
C. `(n_(1)n_(2))/(n_(1) + n_(2)) `
D. `(n_(1) + n_(2))/(n_(1)n_(2)) `

Answer

C

Explanation

Let v be the velocity of sound in air .
`:. n_(1) = v/(2L_(1)) :. L_(1) = v/(2n_(1)) " and " L_(2) = v/(2n_(2)) `
` :. L = L_(1) + L_(2) = v/2 [1/n_(1) + 1/n_(2)]= v/2 ((n_(1) + n_(2)))/(n_(1)n_(2))`
` :. ` New fundamental frequency
`n = v/(2(L_(1) + L_(2))) = (n_(1)n_(2))/(n_(1) + n_(2)) `