In the context of wave functions, what does the trough of a wave refer to?

• A. The lowest point of the wave below the $\mathrm{equilibrium}\mathrm{position}$
• B. The distance between two consecutive $\mathrm{crests}$
• C. The highest point of the wave above the $\mathrm{equilibrium}\mathrm{position}$
• D. The midpoint between a $\mathrm{crest}$ and a $\mathrm{trough}$

Answer: (A)

Verified step by step guidance

1. Understand that a wave oscillates around an equilibrium position, which is the central line where the medium would rest if there were no disturbances.
2. Recognize that the crest of a wave is the highest point above the equilibrium position, representing the maximum positive displacement.
3. Identify that the trough of a wave is the lowest point below the equilibrium position, representing the maximum negative displacement.
4. Note that the distance between two consecutive crests is called the wavelength, which measures the length of one complete wave cycle.
5. Understand that the midpoint between a crest and a trough is the equilibrium position itself, where the displacement is zero.