Bay of Fundy tidal resonance investigation · CAP 2003 #B2
Physics
Problem
Tides are mainly caused by the gradient (or variation) of the gravitational force of the Moon and of the Sun across the Earth's diameter. Large water masses, such as Earth's oceans, bulge along the direction of the gradient and are pinched in the perpendicular direction. As the Earth rotates, the bulges (high tide regions) move across the surface of the Earth.
Now the Bay of Fundy, between New Brunswick and Nova Scotia, is reputed to have the highest tides in the world. Their amplitude is only about a metre at the mouth, or entrance, of the bay, whereas at the other end, 260 km away, the amplitude reaches up to 16 m. You may assume that the relevant speed of water waves in the bay (for very long wavelengths and shallow enough depth) is about 25 m/s. The bay is narrow compared to its length.
Using the above data, investigate whether the unusually high tides could be the result of a resonance excited by the Moon in the bay. Assume that the depth of the bay is uniform, and neglect the influence of the Sun. Hint: calculate the period of the water oscillations in the bay.