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Q.

A closed organ pipe of length L and an open organ pipe contain gases of densities ρ1 and ρ2 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

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a

L3

b

4L3

c

4L3ρ1ρ2

d

4L3ρ2ρ1

answer is C.

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Detailed Solution

Frequency of first over tone of closed pipe = Frequency of first over tone of open pipe⇒3v4L1 = vL2   ⇒ 34L1γPρ1 = 1L2γPρ2∴ L2 = 43Lρ1ρ2               [ ∵ v = γPρ]
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