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Choose the correct alternative (a), (b), (c) or (d) for each of the questions given below :
The distance between successive nodes and anti-nodes is :

A

`lambda/2`

B

`lambda`

C

`lambda/4`

D

`2lambda`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question regarding the distance between successive nodes and anti-nodes, we can break it down into clear steps: ### Step 1: Understanding Nodes and Anti-nodes - In a standing wave, nodes are points where the wave has minimum amplitude (displacement is zero), and anti-nodes are points where the amplitude is maximum (displacement is maximum). - Nodes are typically represented at odd points (1, 3, 5, ...) and anti-nodes at even points (2, 4, 6, ...). ### Step 2: Visualizing the Wave - Let's visualize a standing wave. If we label the nodes and anti-nodes: - Node 1 (N1) - Anti-node 2 (A2) - Node 3 (N3) - Anti-node 4 (A4) - Node 5 (N5) - Anti-node 6 (A6) ### Step 3: Distance Between Nodes and Anti-nodes - The distance between two successive nodes (e.g., N1 and N3) is equal to half the wavelength (λ/2). - The distance between two successive anti-nodes (e.g., A2 and A4) is also equal to half the wavelength (λ/2). - The distance between a node and the nearest anti-node (e.g., N1 and A2) is equal to one-quarter of the wavelength (λ/4). ### Step 4: Conclusion - Therefore, the distance between successive nodes (N1 to N3) is λ/2, and the distance between successive anti-nodes (A2 to A4) is also λ/2. - The distance between a node and the nearest anti-node (N1 to A2) is λ/4. ### Final Answer - The distance between successive nodes and anti-nodes is λ/4.
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