The amplitude of a particular wave is 1 m. The top to bottom (crest to trough) distance of the wave is

Question

BlackTom AI · Accepted Answer

Let's examine what the crest-to-trough distance means and how it relates to amplitude.
Option a: 0.5 m. This would be half of the given amplitude, which does not describe the full crest-to-trough span. Since amplitude is the distance from rest to crest (or rest to trough), the full crest-to-trough distance should be twice the amplitude, not half.
Option b: 1 m. This is equal to the amplitude itself, not the total crest-to-trough distance. The crest-to-trough distance spans from the top of the crest to the bottom of the trough, which covers both positive and negative displacements, i.e., two amplitudes.
Option c: 2 m. Correct: the crest-to-trough distance equals the sum of the crest height above equilibrium plus the trough depth below equilibrium, which is amplitude plus amplitude = 2 × amplitude = 2 m. This matches the given amplitude of 1 m.
Option d: none of these. Since option c is consistent with the physics of amplitude and crest-to-trough distance, this choice is incorrect.
In summary, the crest-to-trough distance is twice the amplitude for a simple sinusoidal wave, and with an amplitude of 1 m, that distance is 2 m.

The amplitude of a particular wave is 1 m. The top to bottom (crest to trough) distance of the wave isSingle choice

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