A standing wave is observed in a string. The distance between the nodes is 0.5 m. The wavelength is therefore:

Question

BlackTom AI · Accepted Answer

Nodes in a standing wave occur at points that remain stationary; adjacent nodes are separated by half a wavelength (λ/2). This is the key relation needed.

1) Relevant knowledge points and concepts
- A standing wave is formed by the superposition of two identical waves traveling in opposite directions.
- Nodes are points of zero amplitude; antinodes are points of maximum amplitude.
- The spatial pattern repeats every half-wavelength: distance between adjacent node–node (or antinode–antinode) = λ/2. Distance between a node and the next antinode = λ/4.

2) Step-by-step reasoning
- The problem gives the distance between nodes = 0.50 m.
- Use the relation: distance between adjacent nodes = λ/2.
- Set up the equation: λ/2 = 0.50 m.

3) Calculations with intermediate steps
- λ/2 = 0.50 m
- Multiply both sides by 2: λ = 2 × 0.50 m
- λ = 1.00 m

4) Why the correct answer is correct
- Since adjacent nodes are separated by half a wavelength, doubling the given node spacing yields the full wavelength. The arithmetic shows λ = 1.00 m, which directly matches option d.

5) Why the other options are incorrect
- a. 0.25 m: This would be λ/4, not λ/2, so it is too small by a factor of 4 relative to the computed wavelength.
- b. 0.5 m: This equals the given node spacing (λ/2), not the full wavelength λ.
- c. 2 m: This is twice the correct wavelength (would correspond to λ = 2.0 m), inconsistent with λ/2 = 0.5 m.

6) Conclusion
- The wavelength is 1.0 m; therefore the correct choice is d. 1 m, which matches the provided answer.

A standing wave is observed in a string. The distance between the nodes is 0.5 m. The wavelength is therefore:单项选择题

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