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 pipe is x 3 L ρ 1 ρ 2 , where x is _______. (Round off to the Nearest Integer)

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 pipe is x 3 L ρ 1 ρ 2 , where x is _______. (Round off to the Nearest Integer),

MARKS App · Accepted Answer

f c = f 0 3 V C 4 L = 2 V 0 2 L ' 3 V C 4 L = V 0 L ' L ' = 4 L 3 V 0 V C = 4 L 3 B . ρ 1 ρ 2 . B ( B is bulk modulus) = 4 L 3 ρ 1 ρ 2 x = 4

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