Study the four transverse waves shown above. Compare the properties of waves B, C, and D to that of wave A, and answer the following question: Compared to wave A, which wave has a shorter wavelength but the same amplitude?

Question

BlackTom AI · Accepted Answer

Wavelength is the horizontal distance between two successive crests (or troughs) and amplitude is the vertical distance from the equilibrium line to a crest (or trough).

1. Relevant knowledge points and concepts
- Wavelength (λ): distance between adjacent crests or troughs along the horizontal axis.  
- Amplitude (A): maximum displacement from the equilibrium (middle) line to a crest (or trough).  
- When comparing waves drawn on the same horizontal scale, count crests or use the small tick marks on the baseline to compare distances.

2. Step-by-step reasoning
- Use the same horizontal reference frame for all waves (the picture shows equally spaced small ticks on each baseline).  
- For wave A, measure the distance from one crest to the next crest: this spans about two tick intervals. That is A’s wavelength. Its crest height above the equilibrium line defines its amplitude.  
- For wave C, measure the distance between successive crests: each crest-to-crest distance spans about one tick interval (roughly half the distance in A). That means C’s wavelength is shorter than A’s. Visually, C has more cycles within the same horizontal length, confirming a shorter λ.  
- Compare amplitudes: the vertical crest height of C from the equilibrium line is visually the same as that of A (same peak displacement). Therefore amplitude of C equals amplitude of A.

3. Intermediate comparisons / calculations
- A: λ ≈ 2 tick units, amplitude = h (some reference height).  
- C: λ ≈ 1 tick unit (shorter), amplitude ≈ h (same as A).  
No numeric computation needed beyond counting tick intervals.

4. Why the correct answer is correct
- Wave C has a clearly shorter crest-to-crest distance than A (shorter wavelength) while its crest height above the equilibrium line matches A’s (same amplitude). Thus C meets both required conditions.

5. Why the other options are incorrect
- Wave B: although its wavelength is shorter (more cycles), its amplitude is smaller than A’s (crests are lower), so amplitude is not the same.  
- Wave D: its wavelength is longer than A’s (fewer cycles stretched out), so it does not have a shorter wavelength even if its amplitude were similar.

6. Conclusion
- Therefore, the wave that has a shorter wavelength but the same amplitude compared to wave A is wave C. This matches the provided answer: wave C.

Study the four transverse waves shown above. Compare the properties of waves B, C, and D to that of wave A, and answer the following question: Compared to wave A, which wave has a shorter wavelength but the same amplitude?单项选择题

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