1.

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 beA. `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» Correct Answer - B
`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))`


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