What is the effect of wave frequency on a ship's GM during heavy seas?

The choice that states the fluctuation of GM (metacentric height) as waves pass, causing instability, is correct because it acknowledges the dynamic nature of a ship's stability in heavy seas. When a vessel encounters waves, particularly in a rough sea state, the ship experiences oscillations or rolling, influenced by the frequency and height of the waves.

As waves pass beneath the ship, the effective center of gravity and buoyancy can shift momentarily, leading to variations in the metacentric height (GM). This fluctuation occurs because the waterline changes while the ship responds to the wave motion; for instance, as a wave lifts the hull, the center of buoyancy changes position. Depending on the ship's design and how it interacts with the waves, this can lead to a reduction in stability, especially if the wave frequency approaches the natural rolling frequency of the vessel.

This dynamic interaction captures the complex relationship between wave frequency and a ship's GM, where inappropriate matching of the ship's roll period with the wave frequency can indeed lead to significant instability. Thus, changes in GM during heavy seas are directly tied to the effects of wave characteristics on the ship’s motion.