Waves

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Waves A wave is a disturbance that travels through space and time. Unlike electromagnetic (optics) waves that can propagate through vacuum, mechanical waves (acoustics, ocean surface waves) need a medium to travel. Waves are characterized by their crests (highs) and troughs (lows), and may be classified as traverse waves with vibrations perpendicular to the direction of propagation (violin strings, light) or longitudinal waves with vibrations parallel to the direction of the propagation (horn, radar). Ripples on the surface of water are a combination of both traverse and Figure 4-6 Operation of a tidal plant (a) During period of high-tides water fills the basin. (b) At low tides the gate is opened and water is allowed to empty into the open sea while turning a turbine. (c) Once all the potential energy is exhausted gates are closed again, allowing water rise in the open sea. (d) The flow is from the open sea to the basin and turbine runs in the opposite direction. (e) The gate is closed until water rises again and repeats the operation. LandOceanGate closedGate closedGate openedGate openedGate openedGate openedGate closedGate closedGate closed(a)(c)(b)(e)(d) Figure 4-7 Tidal power plant at the Bay of Rance estuary in France. 8 Charlier, R. H., “Sustainable co-generation from the tides: A review,” Renewable & Sustainable Energy Reviews, 7, 187-213, 2003. 9 Bernstein, L. B., “Central tidal-power stations in contemporary energy production,” State Publishing House, Moscow, 1961. 10 Frau, J. P., “Tidal energy: promising projects: La Rance, a successful industrial-scale experiment,” IEEE Transactions on Energy Conversion, Volume: 8, Issue: 3, September 1993. pp. 552-558. 11 See the Department of Energy website at http://www.eere.energy.gov/consumerinfo/factsheets/nb1.html. 72 Tides Digging Deeper ... Tides are vertical displacement of water. The action of tides is best understood by examining the law of gravity as stated by the Newton’s Law of Universal Gravitation. According to Newton, any two masses m1 and m2, separated by a distance r, are attracted to each other with a force of where G is the Universal Gravitation constant equal to 6.67x10-11 N.m2/kg2. According to this law, as the moon orbits the earth it is pulled by the earth as though it were connected by a rope to the earth’s center. The pull of gravity becomes weaker at distances farther away from the moon. As result of progressively declining gravity, the earth is stretched along the earth/moon line. Liquids have weaker internal bonds than solids, so ocean water stretches more than land masses. The points on the surface of the earth perpendicular to a line extending between the earth and moon feel less force than the earth’s center. The result is that water is pulled along the moon-earth line and is pushed in the perpendicular direction. The net effect is that water accumulates at both ends along the moon-earth line (high tides). A little more than six hours later the earth has rotated by 90 degrees relative to the moon and the situation reverses (low tides). But what about the pull of the sun? It just so happens that, although the gravitational pull of the sun is much stronger than that of the moon, because the sun is so much farther than the moon, its pull does not change very much from one side of the earth to the other, and its effect is only half that of the moon. The sun, however, gives a helping hand during the new and full moons when it is in line with the earth and the moon. Under these conditions, we have very strong tides which are called spring tides. When the sun, earth and the moon forming a right angle, as is the case during quarter moons, the effect is smallest and we have neap tides.Because the positions of the earth, sun, and moon change every day, tides vary from day to day, and from one location to another. Question: Why do celestial bodies tend to be round? Answer: Gravity pulls all the mass toward the center. Example: Which system experiences a stronger attraction force, the earth-sun or the earth-moon? The sun, earth, and moon have masses of 2x1030, 6x1024, and 7.4x1022 kilograms respectively. The mean distance between the earth and the sun is 1.5x1011 m while the distance between the earth and the moon is 3.84x108 m. Solution: Substitute into equation (iv), we get: F sun-Earth = G = 6.67x10-11 = 3.56x1022 NMS . MErS-E2(2x1030) (6x1024)(1.5x1011)2FMoon-Earth = G = 6.67x10-11 = 2x1020 NMM . MErM-E2(7.4x1022) (6x1024)(3.84x108)2 This calculation shows that the gravitational force of attraction of the sun on the earth is over 177 times that of the moon. As we mentioned above, it is not the absolute force of gravity, but the relative strength of gravitational forces across opposite points on the earth that determines the size of tidal range. (iv) F = Gm1 . m2r2 longitudinal waves. Waves are mathematically represented by their wavelength (l), the distance between two consecutive crests (or troughs), and amplitude, the maximum height between crests and troughs. Period, T, is the time for one complete cycle of a wave oscillation.

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