Discussion
Assertion (A): Waves of different period travel at different speeds in deep water.
Reason (R): The dispersion relation makes celerity depend directly on the wavelength.
Answer: C
Correct answer: Both A and R are true, and R is the correct explanation of A
Both are true and the reason gives the mechanism. In deep water \( \tanh(kd) \to 1 \), so \( C = \sqrt{g/k} = gT/2\pi \) - celerity grows with period. Long swell therefore outruns short waves, which is why a distant storm announces itself first as a long clean swell and only later as a confused sea.
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