Sound WavesHard

Question

A closed organ pipe of radius r1 and an open organ pipe of radius r2 and having same length ′L′ resonate when excited with a given tuning fork. Closed organ pipe resonates in its fundamental mode where as open organ pipe resonates in its first overtone, then : -

Options

A.r2 - r1 = L
B.r2 - r1 = 2/L
C.r2 - 2r1 = 2.5 L
D.2r2 - r1 = 2.5 L

Solution

= L + 0.6 r1
(closed organ pipe)
λ= L + 1.2 r1
(open organ pipe)
⇒ 4 (L + 0.6 r1) = (L + 1.2r2) ⇒ r2 - 2r1 = 2.5 L

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