Concept:Amplitude is a fundamental spatial parameter of a periodic wave, defined as the maximum displacement of any point on the wave from its equilibrium (mean) position.
Formula / Rule / Reaction:$$\text{Amplitude } (A) = \frac{\text{Peak-to-Trough Vertical Height}}{2}$$
Solution:- By definition, amplitude is measured from the central resting equilibrium line (\(y = 0\)) up to the peak of a crest or down to the bottom of a trough.
- In the given wave diagram, the total vertical distance from the bottom of the trough to the peak of the crest is \( 2\text{ m} \).
- Because the equilibrium line divides this peak-to-trough height equally in two:
- $$A = \frac{2\text{ m}}{2} = 1\text{ m}$$
Why other options are incorrect:- Option A (2 m): This is the total peak-to-trough vertical span (total height), which is twice the true amplitude. Confusing peak-to-trough height with amplitude is a classic exam trap.
- Option B (1/2 m) & Option C (\( \frac{\sqrt{3}}{2} \text{ m} \)): Incorrect numerical values that do not correspond to half the measured vertical distance.
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