Wave Shoaling in Shallow Water

Steps:

• Wave speed in water depends on depth via $v = \sqrt{g d}$, where $d$ is water depth.
• As the wave enters shallow water, depth $d$ decreases.
• Thus, speed $v$ decreases proportionally.
• Frequency remains constant because it is set by the wave source and does not change with medium properties.

Why A is correct:

• Speed decreases due to the shallow water approximation formula $v = \sqrt{g d}$; frequency stays constant as waves maintain their oscillation rate from the source.

Why the others are wrong:

• B: Speed actually decreases, not increases, in shallower depths.
• C: Speed decreases, it does not stay constant.
• D: Frequency stays constant, it does not increase.

Final answer: A