Question 257: Waves

Question

In a pipe closed at one end, air column is vibrating in its second overtone. The column has

Accepted Answer

We are dealing with a
pipe closed at one end (closed organ pipe)
.
Key points:
In a closed organ pipe, the closed end is always a
node
, and the open end is always an
antinode
.
Only
odd harmonics
are possible:
1st harmonic (fundamental: $n=1$)
2nd harmonic (first overtone, $n=3$)
3rd harmonic (second overtone, $n=5$)
For the $n=5$ mode (second overtone), the standing wave inside the pipe will have multiple nodes and antinodes.
Determining the pattern:
For the $n = 5$ mode in a closed pipe, the pattern corresponds to $ 	frac{5}{4} \lambda$.
That means the pipe length contains 5 quarter wavelengths.
Each quarter wavelength segment contains
either a node or an antinode
alternately.
Starting from the closed end = node Ã¢ÂÂ AÃ¢ÂÂNÃ¢ÂÂAÃ¢ÂÂ¦ until open end = antinode.
So, for 5 quarter wavelengths, we get:
Node (at closed end)
Antinode
Node
Antinode
Node
Antinode (at open end)
Thus:
Nodes = 3
Antinodes = 3
Ã¢ÂÂ Correct Answer:
Option A: three nodes and three antinodes.

Answer

three nodes and three antinodes.

Answer

three nodes and four antinodes.

Answer

two nodes and three antinodes.

Answer

four nodes and three antinodes.

Waves

In a pipe closed at one end, air column is vibrating in its second overtone. The column has

Choose the correct answer: