A closed organ pipe of length L and an open organ pipe contain gases of densities ρ$$1$$ and ρ$$2$$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open organ pipe is: (neglect$$ the end $$correction)

Question

A closed organ pipe of length  L and an open organ pipe contain gases of densities ρ$$1$$ and ρ$$2$$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open organ pipe is: (neglect$$ the end $$correction)

Infinity Learn · Accepted Answer

GivenLength of closed organ $$pipe=$$ LDensity of gases,  ρ$$1$$ and ρ$$2$$ respectivelyFrequency of first over tone of closed organ pipe $$=$$ Frequency of first over tone of open organ pipe ⇒$$3v14L1=2v22L2$$⇒$$34L1$$γPρ$$1=1L2$$γPρ$$2$$ As $$v=$$γPρ⇒$$L2=4L13$$ρ$$1$$ρ$$2=4L3$$ρ$$1$$ρ$$2$$

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