Wave Theories and Transformation Questions and Answers

Answer: C

Orbital diameter decays exponentially with depth and is negligible below half a wavelength. In shallow water the orbits flatten into ellipses and become horizontal at the bed. The bed forces the vertical motion to vanish at the boundary.

Answer: D

Both are true and the reason gives the decay, and this is precisely the basis of the deep water criterion. Submarines and moored structures below that depth feel comparatively little wave action. Half a wavelength is the practical limit of wave influence.

Answer: A

The progression reflects the influence of the bed on the flow field beneath the wave. Sediment movement begins once the near-bed orbital velocity exceeds the threshold for the grain size present. Near-bed velocity is the link between waves and sediment.

Answer: B

Individual crests move at the celerity while the group and its energy move more slowly in deep water. This is why crests appear to run forward through a group and vanish at its front. Energy stays with the group rather than with a crest.

Answer: C

Correct answer: one half

In deep water \( C_g = C/2 \), so energy travels at half the speed of the individual crests - waves appear at the rear of a group, run through it and vanish at the front. In shallow water the two become equal, and it is this change that drives shoaling.

Answer: D

The ratio of group velocity to celerity rises from one half in deep water to one in shallow water. Waves and their energy therefore travel together once the depth becomes small. Shallow water removes the distinction entirely.

Answer: A

Both are true and the reason gives the kinematics, and crests appear at the rear and disappear at the front. The group as a whole carries the energy at the slower speed. Only the group velocity matters for energy transport.

Answer: B

Total energy per unit area is one eighth of rho g H squared, split equally between kinetic and potential. Doubling the wave height therefore quadruples the energy the wave carries. Loading on a structure scales with the energy, not the height.

Answer: C

Energy varies with the square of the height, so doubling gives four times as much. This is why modest increases in wave height produce large increases in the loading on a structure. Design is therefore sensitive to the height estimate.

Answer: D

Both are true and the reason gives the equal partition, which is a general property of linear oscillatory systems. The total is therefore one eighth of rho g H squared. Equipartition is a general result for linear wave systems.