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此套试卷由25道选择题以及3道大题组成
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Part A选择题部分:
Part B简答题部分
Solution to Problem 2:
If the high tides in the Bay of Fundy are caused by a resonance mechanism, it must be because the tidal forces from the Moon driving seawater in and out of the bay are exciting one of its standing-wave modes. The rise and fall of the tide can be modelled by a wave with extremely long wavelength propagating on the water. The boundary conditions at the mouth and the far end of the bay mimic those of a standing wave on a string with on end fixed (mouth), where the vertical displacement is minimum, and the other free (far end), where displacement is maximum. This mode would have a wavelength入 =4L, where L is the length of the string or, here, the length of the bay: L = 260 km. With v = 25 m/s the speed of the waves, their period is
Now we expect the period of the tides to be about 12.4 hours. Indeed, if the Moon had a fixed position with respect to the Earth, the two tidal bulges (high tides) on Earth would move in the direction opposite the Earth’s rotation with one passing through a given position every 12 hours. But the Moon moves in its own orbit with the Earth’s rotation with an average period of about 29 days, ie. 6.20 in the sky every 12 hours or 720 minutes. Therefore, it takes 25 minutes for the Moon to cover that angular distance, and this increases the tidal period to 12.4 hours. We have found that the period with which the water sloshes back and forth in the bay due to the Moon’s tidal force is comparable to the period of the fundamental resonance mode for our admittedly crude model of the Bay of Fundy. Given the approximations involved, this is quite a good match, and it is likely that this resonance mechanism can explain why the tides are amplified.
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