Physics

Problem

Ocean surface waves produced by a distant storm travel into a coastal region where the water depth decreases abruptly at a sandbar. In deep water (medium 1) the waves move at

16\,\text{m\,s}^{-1}

and have a wavelength of

22\,\text{m}

. Upon crossing onto the sandbar (medium 2), their speed drops to

12\,\text{m\,s}^{-1}

while the frequency set by the storm remains unchanged. (a) Calculate the new wavelength of the waves in medium 2. (b) Determine the ratio

\lambda_{2}/\lambda_{1}

, where

\lambda_{1}

is the deep-water wavelength and

\lambda_{2}

is the wavelength over the sandbar. Interpret the meaning of this ratio in the context of wave behaviour at the boundary. (c) A floating marker is anchored just beyond the sandbar in medium 2. How many crests pass the marker in

5.0\,\text{min}

? Show your reasoning.

Intuitive explanation

This is a wave refraction problem where the key insight is that frequency is the storm's "metronome"—it never changes as waves cross boundaries. Since $v = f\lambda$ , when speed decreases, wavelength must shrink proportionally to keep frequency constant. Use the unchanged frequency to find the new wavelength in shallow water, just like how light bends when entering a denser medium.

Intuitive explanation

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