Question

A Closed organ pipe (closed at one end) is excited to support the third overtone. It is found that air in the pipe has
A. Three nodes and three antinodes
B. Three nodes and four antinodes
C. Four nodes and three antinodes
D. Four nodes and four antinodes

Answer 1

Hint: When a closed pipe vibrates in fundamental mode then there are one node and one antinode formed. Similarly, when it vibrates in the first overtone then there are two nodes and antinodes formed and so on. By using this concept, we can get the result of the third overtone.






Complete answer:
As we know that in an organ pipe, the waves form at a closed side of the pipe is known as nodes and on the open side known as antinodes. Also, between the two ends nodes and antinodes are formed.
In this question, it is given that a closed organ pipe which is closed at one end and open at another is excited to support the third overtone. The third overtone also called forth harmonic which means that the total number of cycles must be four nodes.
Now look at the figure, for fourth harmonic the organ pipe contains four nodes. If we count number of nodes and antinodes, we get four nodes and four antinodes.

Image: A one side open and one side closed organ pipe for third overtone.
Hence option D is the correct answer









Note: The lowest natural frequency of a system is known as Fundamental frequency whereas the higher frequencies are known as Overtones. The node is defined as the point on the wave where resultant amplitude is zero while antinodes are those points where resultant amplitude is maximum.