Consider a water wave with wavelength ten meters and amplitude 10 centimeters (s

Question

Consider a water wave with wavelength ten meters and amplitude 10 centimeters (so trough to peak elevation difference is 20 centimeters). Find the magnitude of the horizontal acceleration beneath the steepest part of the wave, say at about approximately 30 centimeters below the surface. Submit the answer in units of m s-2.

Hint: The key to finding the horizontal acceleration is to use fact that the pressure field beneath the wave is very close to the hydrostatic prediction, for depths much less than the wavelength, as is the case here.

Explanation / Answer

   The wavelength of the water wave, ? = 10 m    The amplitude is given by, A = 10 cm = 10-1 m    If the wavelength is 10 m then the speed of water wave, v = 4 knts = 2.056 m/s                                             ? = (2pv) / ?                                             ? = 2(3.14)(2.056) / 10 = 1.3 rad / sec    The horizontal acceleration, a = A?2 = 10-1(1.3)2 = 0.169 m/s2                                             ? = (2pv) / ?                                             ? = 2(3.14)(2.056) / 10 = 1.3 rad / sec    The horizontal acceleration, a = A?2 = 10-1(1.3)2 = 0.169 m/s2                                             ? = 2(3.14)(2.056) / 10 = 1.3 rad / sec    The horizontal acceleration, a = A?2 = 10-1(1.3)2 = 0.169 m/s2

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