Wave Kinematics and Dynamics Questions and Answers

Answer: B

The wave amplitude increases and wave length decreases.

The tidal wave in an estuary is a long (shallow water) wave, travelling at c = √(gh). As the depth h decreases the wave slows down. Its period is fixed by the forcing, so its wavelength, cT, shortens.

Without friction the energy flux is conserved. As the wave slows, the energy bunches up and the amplitude grows; in a channel of constant width it varies as h^-1/4 (Green's law). The other options get one or both trends backwards.

Answer: B

The key's answer is 1 hour 30 minutes, taking a typical open-ocean depth of about 4 km.

A tsunami's wavelength is far greater than the ocean depth, so it travels as a shallow-water wave whose speed depends only on depth d:

\[ \begin{aligned} v &= \sqrt{g d} = \sqrt{9.8 \times 4000} \\ &\approx 198\ \mathrm{m/s} \approx 713\ \mathrm{km/h} \\ t &= \frac{1100}{713} \approx 1.5\ \text{h} \end{aligned} \]

The depth is not stated in the question, so the answer depends on assuming this typical depth; it agrees with the usual figure of 700 to 800 km/h for tsunamis in the deep ocean. One hour would need a speed of 1100 km/h (a depth of about 9.5 km), and two hours or more would need depths of about 2.4 km or less.