The image below shows a typical wave. Identify part B.

Question

BlackTom AI · Accepted Answer

The labeled segment B measures the horizontal distance from a crest to the adjacent trough, which equals half a wavelength.

1) Relevant concepts
- Wavelength (λ): the spatial period of the wave, distance between successive equivalent points (e.g., crest-to-crest or trough-to-trough).
- Half-wavelength (λ/2): distance between a crest and the next trough (or vice versa).
- Amplitude: vertical displacement from the equilibrium (midline) to a crest (or trough).
- Frequency: number of complete cycles per unit time (not a spatial distance).

2) Step-by-step reasoning
- In the diagram, A spans from one crest to the next crest; that is the full wavelength λ.
- B spans from a crest to the immediately following trough. By definition, that is half of the full cycle in space.
- A sinusoidal wave completes one full spatial cycle when the phase advances by 2π; a crest and the next trough are separated by a phase difference of π (half the cycle), therefore they are separated by half the spatial period.

3) Mathematical intermediate steps (using a sinusoid)
- For y = A sin(kx − ωt), wavelength λ = 2π / k.
- Phase difference between crest and trough = π, so spatial separation Δx = π / k.
- Substitute k: Δx = π / k = π / (2π/λ) = λ/2.

4) Why the correct answer is correct
- Both the visual evidence (crest-to-trough distance) and the phase/period analysis show B = λ/2 (half a wavelength).

5) Why the other options are incorrect
- "2 wavelengths": twice as long as A, not the short crest-to-trough distance shown.
- "Amplitude": a vertical measure (like arrow C), not a horizontal distance.
- "Wavelength": that is A (crest-to-crest), not B.
- "Frequency": a temporal rate (cycles per second), not a spatial length.

6) Conclusion
Therefore, part B represents a half wavelength, which confirms the provided answer: Half wavelength.

The image below shows a typical wave. Identify part B.单项选择题

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