The air column in an organ pipe, which is closed at one end, is vibrating in such a way as to produce the second harmonic. A pressure node and displacement node, respectively, occur at
A) 1 and 3.
B) 1 and 5.
C) 7 and 4.
D) 7 and 5.
E) 5 and 3.

Question

The air column in an organ pipe, which is closed at one end, is vibrating in such a way as to produce the second harmonic. A pressure node and displacement node, respectively, occur at
A) 1 and 3. 
B) 1 and 5. 
C) 7 and 4. 
D) 7 and 5. 
E) 5 and 3.

Quizplus · Accepted Answer

For a closed pipe, the second harmonic wavelength is equal to twice the length of the pipe. Therefore, there are two "quarters" in the pipe, with one pressure node and one displacement node at each quarter. Since the pipe is closed at one end, there is a pressure node at the closed end, which is a quarter wavelength from the open end. This means that the pressure node occurs at the 3/4 mark of the pipe length. Similarly, there is a displacement node at the open end, which is also a quarter wavelength from the closed end, so it occurs at the 1/4 mark of the pipe length. Therefore, the pressure node and the displacement node occur at positions 7 and 5, respectively. Thus, the answer is D.

The Air Column in an Organ Pipe, Which Is Closed