Which of the following statements concerning why tsunamis build in height as they approach a coastline is FALSE?

Question

BlackTom AI · Accepted Answer

Shoaling of long waves causes amplitude growth through conservation of wave energy as wave speed decreases in shallow water; simply "feeling" the seafloor is not by itself the direct and immediate cause claimed in the statement.

Relevant concepts:
- Shallow-water wave speed: c = sqrt(g h), where g is gravity and h is depth.
- Wave energy density (per unit horizontal area) for small-amplitude waves: E = (1/8) ρ g H^2, where H is wave height.
- Energy flux F = E · c. If energy flux is approximately conserved as the wave shoals, changes in c force changes in H.
- A wave "feels" the seafloor when depth is on the order of (about 1/2) its wavelength; shoaling (reduction in c and λ) then occurs as depth decreases further.

Step-by-step reasoning (with intermediate steps):
1. c = sqrt(g h). As h decreases near shore, c decreases.
2. E = (1/8)ρ g H^2, so flux F = E c = (1/8)ρ g H^2 c. If F ≈ constant, then H^2 c = constant → H ∝ c^(-1/2).
3. Since c ∝ h^(1/2), H ∝ (h^(1/2))^(-1/2) = h^(-1/4). Thus as depth h decreases, H increases (shoaling), but the increase follows the chain: reduced depth → reduced speed c → reduced wavelength λ = cT → energy concentrated into smaller horizontal space → increased H.
4. The phrase "first begins to ‘feel’ the seafloor which consequently increases its height" implies that the act of "feeling" the bottom alone directly inflates height. In fact, "feeling" is the threshold where bottom effects begin; the height increase results from the subsequent slowing, wavelength shortening, and energy concentration (shoaling) — not an instantaneous direct effect of feeling.

Why the correct answer is correct (i.e., why that option is FALSE):
- The option misstates causality: feeling the seafloor is a condition that permits shoaling, but it is the reduction in wave speed and geometrical confinement (and energy conservation) that actually increases wave height. Saying feeling the seafloor "consequently increases its height" is therefore inaccurate.

Why the other options are true:
- Enclosed harbors and bays can focus and amplify tsunami heights by resonance and geometric constriction (true).
- Slowing and wavelength shortening do force height increase via energy conservation (true).
- Shallowing and the piling of water against the shore are physical descriptions of why tsunami waves grow in height near coasts (true).

Conclusion: The statement "As they approach the shore, the tsunami first begins to ‘feel’ the seafloor which consequently increases its height." is false for the reasons above, so the provided answer is confirmed.

Which of the following statements concerning why tsunamis build in height as they approach a coastline is FALSE?单项选择题

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