In the third normal mode of vibrationn of a closed organ pipe, the number of nodes and antinodes respectively are

Options

A. 4,3
B. 3,4
C. 3,3
D. 4,4

Explanation

To solve the problem of determining the number of nodes and antinodes in the third normal mode of vibration of a closed organ pipe, we can follow these steps:

### Step 1: Understand the structure of a closed organ pipe
A closed organ pipe has one end closed (node) and the other end open (antinode). The closed end will always have a node, where the displacement of air is zero, while the open end will have an antinode, where the displacement is maximum.

**Hint:** Remember that closed ends have nodes and open ends have antinodes.

### Step 2: Identify the normal modes of vibration
In a closed organ pipe, the normal modes of vibration can be represented as follows:
- The first normal mode (fundamental frequency) has 1 node (at the closed end) and 1 antinode (at the open end).
- The second normal mode has 2 nodes and 1 antinode.
- The third normal mode has 3 nodes and 2 antinodes.

**Hint:** Each successive normal mode adds one additional node and one additional antinode.

### Step 3: Analyze the third normal mode
In the third normal mode of vibration:
- The closed end still has 1 node.
- There will be additional nodes along the length of the pipe. For the third mode, we will have a total of 3 nodes.
- The open end will have 1 antinode, and there will be additional antinodes in between. For the third mode, we will have a total of 3 antinodes.

**Hint:** Count the nodes and antinodes carefully in the diagram of the third normal mode.

### Step 4: Conclusion
From the analysis, we conclude that in the third normal mode of vibration of a closed organ pipe, there are:
- **Number of nodes:** 3
- **Number of antinodes:** 2

Thus, the answer is:
- **Nodes:** 3
- **Antinodes:** 2

### Final Answer
The number of nodes and antinodes in the third normal mode of vibration of a closed organ pipe are 3 and 2, respectively.

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