Two closed organ pipe A and 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

Options

A. `V_(A)=V_(B)`
B. `V_(A) gt V_(B)`
C. `V_(A) lt V_(B)`
D. Either (b) or (c ) depending on the ratio of their diameters

Answer

C

Explanation

In the fundamental mode of vibration, `(lambda)/(4)=(l+0.3d)`
where, 0.3 d is the necessary end correction.
Frequency of vibration, `nu`
`=(v)/(lambda)=(v)/(4(l+0.3d))`
As `l` is same for both pipes, wider pipe (A) will resonate at a lower frequency, i.e. `v_(A) lt v_(B)`.