Ocean surface waves produced by steady winds involve orbital motion of water particles that has both horizontal and vertical components. A team of marine physicists wants to know whether such surface waves can be polarized by forcing them through a long, narrow channel whose width can be adjusted.
Assume deep-water conditions where the wavelength λ is much smaller than the water depth, and the channel width can be varied from 5m down to 0.5m while keeping the wave amplitude small compared with λ.
(1) Discuss whether surface waves on deep water are purely transverse, purely longitudinal, or a combination of both. Support your answer with reference to particle trajectories.
(2) Explain whether it is theoretically possible to obtain a state analogous to polarization for these water waves by narrowing the channel.
(3) If the team nonetheless observes a reduction in wave amplitude when the channel is made very narrow, provide two plausible physical explanations that do NOT rely on true polarization of the wave.
(4) Suggest an experimental measurement (other than amplitude) that the team could perform to confirm whether any component of the wave motion has been preferentially filtered by the channel walls.