Question

In an organ pipe closed at one end produces a fundamental note of frequency '\(ν\)'. The pipe is cut into two pipes of equal length. The fundamental frequencies produced in the two pipes are

• A. \(ν\) , \(2ν\)
• B. \(\frac{ν}{2}\) , \(ν\)
• C. \(2ν\) , \(4ν\)
• D. \(\frac{ν}{2}\) , \(2ν\)

Hint:

A closed pipe has fundamental v/4L. Cut in half, one half is still closed and the other is open at both ends.

Answer 1

The Correct Option is C

Step 1: Note the two end conditions:
The original closed pipe has one closed end and one open end. Cutting it in the middle gives one piece with the closed end and an open cut end (closed-open type), and another with two open ends (open-open type).

Step 2: Compute with $\nu = \frac{v}{4L}$:
Closed-open piece of length $\frac L2$: $\frac{v}{4(L/2)} = \frac{2v}{4L} = 2\nu$.
Open-open piece of length $\frac L2$: $\frac{v}{2(L/2)} = \frac{v}{L} = 4\nu$.

Step 3: Result:
The frequencies are $2\nu$ and $4\nu$.

Final Answer:
Option (C). \[ \boxed{2\nu,\ 4\nu \text{ (C)}} \]