Your Answer : (Not Answered)

Correct Answer : C

Wave refraction concentrates energy on headlands and disperses it across bays.

Waves slow down as they enter shallow water. Off a headland the water shallows first, so the part of the wave crest approaching it slows and the crest bends to wrap around the headland. Wave rays (orthogonals) converge on the headland, focusing energy there, and diverge in the deeper water of the bays, spreading the energy thinly.

That is why headlands are eroded while bays fill with beaches, and why an irregular coast tends to be straightened over time. Refraction therefore does control the distribution of energy, and it does not spread it equally or concentrate it in the bays.

Your Answer : (Not Answered)

Correct Answer : B

Such a series of waves is a tsunami.

A tsunami is generated when a large volume of ocean water is suddenly displaced, most often by an undersea earthquake, but also by submarine landslides or volcanic eruptions. The waves travel across oceans at several hundred kilometres per hour with long wavelengths, and grow in height as they reach shallow coastal water, as in the Indian Ocean tsunami of December 2004.

Storms and hurricanes are atmospheric systems that create wind-driven waves and surges, and a flood is an overflow of water onto land; none is a wave train caused by displacement of the water body itself.

Your Answer : (Not Answered)

Correct 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.

Your Answer : (Not Answered)

Correct Answer : A

Wave speed or celerity is C = L/T.

A wave advances one wavelength L in one wave period T, so its speed is the distance covered divided by the time taken. For example, a wave 100 m long with a period of 8 s travels at 12.5 m/s. In deep water the period alone fixes the speed, \(C \approx 1.56\,T\) m/s, because the wavelength depends on the period.

T/L has units of time per distance, and L×T has units of distance times time, so neither can be a speed. Wave height H does not set the speed of a wave in this relation.

Your Answer : (Not Answered)

Correct Answer : C

The speeds are approximately 10, 31 and 100 m s^-1.

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

\[ \begin{aligned} c &= \sqrt{gh} \\ \sqrt{9.81 \times 10} &\approx 9.9\ \text{m/s} \\ \sqrt{9.81 \times 100} &\approx 31.3\ \text{m/s} \\ \sqrt{9.81 \times 1000} &\approx 99\ \text{m/s} \end{aligned} \]

Speed rises with depth, so the options with speeds falling as depth increases, or out of order, are wrong; 50, 75 and 100 m s^-1 does not follow the square-root law. This depth dependence is why a tsunami slows and steepens as it reaches shallow coastal water.

Your Answer : (Not Answered)

Correct Answer : B

The key gives Semidiurnal and Mixed.

Tides along the west coast of India have two high and two low waters each day, so they are semidiurnal in character, but the two highs (and the two lows) are of markedly unequal height. That inequality, which grows northward towards the Gulf of Khambhat and Kutch, is what defines a mixed, predominantly semidiurnal tide.

A diurnal tide has only one high and one low water a day, which does not describe the Indian west coast, so options containing 'Diurnal' are wrong. 'Only Mixed' drops the semidiurnal character that dominates along much of the coast.

Your Answer : (Not Answered)

Correct Answer : B

The answer is wind-induced waves, astronomical tides, and distant cyclonic storm.

The total water level at the coast during a cyclone is the sum of three parts: the astronomical tide at that moment; the storm surge, the rise produced by the cyclone's winds piling water against the coast and its low pressure lifting the sea surface (the 'cyclonic storm' contribution); and the set-up and run-up of the wind-generated waves breaking on the shore. The worst flooding comes when a large surge arrives at high tide with heavy waves on top.

The option with tides and the storm alone leaves out wave set-up. Coastal currents and river flow can matter locally, but they are not among the standard components of the storm water level, so the options substituting them for wind waves are incomplete.

Your Answer : (Not Answered)

Correct 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.