ANSWERS TO STUDY QUESTIONS CHAPTER 10

1. They are equal.

2. The shorter the wavelength, the more rapidly orbital size diminishes with depth.

3. 1 to 7 height to length ratio

4. C = L/T    L = 100m and T = 10sec, so C = 100m/10sec = 10m/sec (that’s 36 km/hr or 22 mi/hr)

5. The wave will white-cap, converting wave energy into turbulence and ultimately random molecular motion (heat).

6. Waves that have traveled a long way from their source will have undergone much dispersion. They should therefore be well organized into swell - waves of nearly identical periods and wavelengths traveling together. They will also be traveling in pretty much the same direction. For a nearby source there would be little chance for dispersion to occur so consequently the waves would be more chaotic - waves of many different periods and wavelengths all superimposed on one another. Wave directions would vary more for a nearby source as well. Assuming both sources (storms) were the same intensity, waves arriving from a distant source will be smaller in height, so that only the largest and therefore longest waves would probably be observed.

7. The first waves to arrive from a new swell will be those that outran the rest of the swell. They will therefore have relatively long wavelengths and periods, but because they left most of the other waves behind, such waves will have few other waves to constructively interfere with and will consequently be small. However, over the first day or two of the swell, wave heights should build rapidly. Each wave that arrives should theoretically be slower and therefore of shorter period and wavelength than the wave that preceded it. You might expect the height of these slower waves to decrease (since, in a “sea”, wave height is directly proportional to wavelength), but average wave heights increase as more constructive interference takes place. Wave heights will peak when the optimal combination of wavelength and interference occurs - usually this happens on the second day of a new swell. After that, wave heights, periods and lengths will all decrease gradually. Eventually the waves will be so small as to go undetected.

8. The velocity of a wave train (group velocity) is half the velocity of the waves that comprise it.

9. Waves occur in sets due to mixed interference. When waves of different lengths (or periods) interfere they will be in phase (constructive interference) in some places, but out of phase (destructive interference) in other places. If this happens in deep water, the slightly different velocities of the component waves gradually changes their phase as fast waves either catch-up with slow waves or outrun them. Thus the leading wave in a wave train will die out but a new wave will take its place at the rear of the train. Near shore in shallow water, the depth (which is the same for each component wave) controls wave velocity and keeps the waves locked either in phase (the set) or out of phase (the lull).

10. velocity decreases, length decreases, height increases, steepness increases, orbits flatten

11. one half their wavelength

12. Waves usually break in a depth of water equal to 1.3 times their height. For example: A 10-foot high wave normally breaks in about 13 feet of water.

13. The velocity (celerity) of a deep water wave is controlled by it’s length (or period).

14. Water depth controls the velocity (celerity) of a shallow water wave.

15. The velocity (celerity) for any wave can be calculated by dividing it’s length by it’s period. C = L/T

16. Plunging waves occur where the bottom abruptly shallows, like over a rock or coral reef.

17. Spilling waves occur where the bottom gradually shallows, like on most sandy beaches.

18.    dispersion - separation of waves into different wavelengths as long waves outrun shorter ones. It happens as waves leave a "sea", changing their initial chaotic state into progressively more ordered swell.

refraction - change in wave direction due to change in wave velocity. It happens to ocean waves when one end is in shallow water while the other’s in deep.

reflection - the bouncing-off of wave energy. It happens when waves encounter a steeply sloping obstacle such as a breakwater or seawall.

diffraction - the lateral transfer of wave energy. It happens when waves go through a gap in a breakwater.