Q. Two closed organ pipe A and pipe B have the same length. A is wider than B. they resonate in the fundamental mode at frequencies $v_{A}and\ v_{B}$respectively, then
A) $v_{A} = v_{B}$
B) $v_{A} > v_{B}$
C) $v_{A} < v_{B}$
D) Either (b) or (c) depending on the ratio of their diameters
Explanation
(c) In the fundamental mode of vibration
$\frac{\lambda}{4} = (l + 0.3d)$
Where 0.3d the necessary end correction. frequency of vibration,
$v = \frac{v}{\lambda} = \frac{v}{4(l + 0.3)}$
As 𝒍 is same for both pipes, wider pipe (A) will resonate at a lower frequency, i.e., $v_{A} < v_{B}.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.