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

Options

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

Answer

B

Explanation

`upsilon_(1)=v/(2L_(1))`..(i)
`upsilon_(2)=v/(2L_(2))`…(ii)
When two pipes are joined in series, the fundamental frequency of the new pipe is
`upsilon=v/(2(L_(1)+L_(2))=v/(2L_(1)+2L_(2))`
`=v/(v/(upsilon_(1))+v/(upsilon_(2)))` 0=(Using (i) and (ii))
`=(upsilon_(1)upsilon_(2))/(upsilon_(2)+upsilon_(1))`