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: (neglect the end correction)
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a
L3
b
4L3
c
4L3ρ1ρ2
d
4L3ρ2ρ1
answer is C.
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Detailed Solution
GivenLength of closed organ pipe= LDensity of gases, ρ1 and ρ2 respectivelyFrequency of first over tone of closed organ pipe = Frequency of first over tone of open organ pipe ⇒3v14L1=2v22L2⇒34L1γPρ1=1L2γPρ2 As v=γPρ⇒L2=4L13ρ1ρ2=4L3ρ1ρ2