Question

A pipe closed at one end produces a fundamental note of frequency '\(\nu\)'. The pipe is cut into two pipes of equal lengths. The fundamental frequencies produced in the two pipes are

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

Hint:

After cutting, one piece is closed at one end and the other is open at both ends.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
A closed pipe of length \(L\) has \(\nu=\dfrac{v}{4L}\). An open pipe of length \(L\) has \(\nu=\dfrac{v}{2L}\).

Step 2: After cutting
Each piece has length \(L/2\). The piece with the closed end is still closed at one end: \(\nu_1=\dfrac{v}{4(L/2)}=2\nu\).

Step 3: The other piece
The other piece is open at both ends: \(\nu_2=\dfrac{v}{2(L/2)}=\dfrac{v}{L}=4\nu\).

Final Answer:
The two fundamental frequencies are \(2\nu\) and \(4\nu\). \[ \boxed{\text{(D) }2\nu,\,4\nu} \]