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Two open organ pipesof fundamental frequ...

Two open organ pipesof fundamental frequencies `n_(1) and n_(2)` are joined in series. The fundamental fre-quency of the new pipe so obtained will be :

A

`(n_(1) + n_(2))`

B

`(n_(1) + n_(2))/(2)`

C

`sqrt(n_(1)^(2) + n_(2)^(2))`

D

`(n_(1)n_(2))/(n_(1)+n_(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`n_(1) = (V)/(2l_(1))`
`:. l_(1) = (V)/(2n_(1)):" similarly " l_(2) = (V)/(2n_(2))`
`:. l_(1) + l_(2) = (V)/(2) ((1)/(n_(1))+(1)/(n_(2))) = (V(n_(1) + n_(2)))/(2n_(1)n_(2))`
Fundamental frequency in joined open pipe
`n = (V)/(2(l_(1)+l_(2)))=(V)/(2)*(2n_(1)n_(2))/(V(n_(1)+n_(2)))= (n_(1)n_(2))/(n_(1)+ n_(2))`
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