Question

The INCORRECT statement is

• A. The separation between two successive nodes is λ
• B. Antinodes are formed at both ends of an open organ pipe
• C. In a one end closed organ pipe node is formed at the closed end
• D. Nodes are formed at both ends of steched string
• E. The separation between the successive node and antinode is \(\frac{\lambda}{4}\)

Answer 1

The Correct Option is A

The separation between two successive nodes is not equal to the wavelength \( \lambda \), but half of the wavelength \( \lambda/2 \). This is because nodes in standing waves are separated by half the wavelength, as seen in the harmonic wave pattern. Therefore, statement (A) is incorrect. The other statements are correct:

• In an open organ pipe, antinodes are indeed formed at both ends.
• In a one-end closed organ pipe, a node is formed at the closed end, and an antinode is formed at the open end.
• For a stretched string, nodes are formed at both ends.
• The separation between the successive node and antinode is \(\frac {\lambda}{4}\), which is a characteristic of standing wave patterns.

The correct option is (A) : The separation between two successive nodes is \(λ\)

Answer 2

Let's analyze each statement: 
 
1. The separation between two successive nodes is \( \lambda \):
❌ Incorrect. The distance between two successive nodes in a stationary wave is \( \frac{\lambda}{2} \), not \( \lambda \). 

2. Antinodes are formed at both ends of an open organ pipe:
✅ Correct. In an open organ pipe, both ends are antinodes. 

3. In a one end closed organ pipe, node is formed at the closed end:
✅ Correct. Closed end is always a node due to zero displacement. 

4. Nodes are formed at both ends of stretched string:
✅ Correct. Both ends of a fixed string are nodes. 

5. The separation between the successive node and antinode is \( \frac{\lambda}{4} \):
✅ Correct. This is true by wave nature. 

Therefore, the INCORRECT statement is:
The separation between two successive nodes is \( \lambda \)