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Investigate the motion of waves in water, what happens when waves get reflected and different types of superposition of waves with this guide for KS3 physics students aged 11-14 from BBC...
- BBC Bitesize
They carry energy. A wave transfers energy from one place to...
- BBC Bitesize
They carry energy. A wave transfers energy from one place to another. Examples of waves include: water waves, sound waves, light waves, radio waves, microwaves, x-rays, ultrasound waves and...
Water waves moving from shallow to deeper water. Light waves will speed up or slow down when they enter or exit a material of a different optical density, which is the refractive index of the material.
Although waves can travel over great distances, the water itself shows little horizontal movement; it is the energy of the wave that is being transmitted, not the water. Instead, the water particles move in circular orbits, with the size of the orbit equal to the wave height (Figure 10.1.3).
- Overview
- Physical characteristics of surface waves
- Wave types
- Wind waves and swell
- Wind surges
- Waves of seismic origin
- Standing waves, or seiches
- Internal waves
wave, a ridge or swell on the surface of a body of water, normally having a forward motion distinct from the oscillatory motion of the particles that successively compose it. The undulations and oscillations may be chaotic and random, or they may be regular, with an identifiable wavelength between adjacent crests and with a definite frequency of os...
There are two physical mechanisms that control and maintain wave motion. For most waves, gravity is the restoring force that causes any displacements of the surface to be accelerated back toward the mean surface level. The kinetic energy gained by the fluid returning to its rest position causes it to overshoot, resulting in the oscillating wave motion. In the case of very short-wavelength disturbances of the surface (i.e., ripples), the restoring force is surface tension, wherein the surface acts like a stretched membrane. If the wavelength is less than a few millimetres, surface tension dominates the motion, which is described as a capillary wave. Surface gravity waves in which gravity is the dominant force have wavelengths greater than approximately 10 cm (4 inches). In the intermediate length range, both restoring mechanisms are important.
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A wave’s amplitude is the maximum displacement of the surface above or below its resting position. The mathematical theory of water wave propagation shows that for waves whose amplitude is small compared to their length, the wave profile can be sinusoidal (that is, shaped like a sine wave), and there is a definite relationship between the wavelength and the wave period, which also controls the speed of wave propagation. Longer waves travel faster than shorter ones, a phenomenon known as dispersion. If the water depth is less than one-twentieth of the wavelength, the waves are known as long gravity waves, and their wavelength is directly proportional to their period. The deeper the water, the faster they travel. For capillary waves, shorter wavelengths travel faster than longer ones.
Waves whose amplitude is large compared with their length cannot be so readily described by mathematical theory, and their form is distorted from a sinusoidal shape. The troughs tend to flatten and the crests sharpen toward a point, a shape known as a conoidal wave. In deeper water the limiting height of a wave is one-seventh of its length. As it approaches this height, the pointed crests break to form whitecaps. In shallow water the long-amplitude waves distort, because crests travel faster than troughs to form a profile with a steep rise and slow fall. As such waves travel into shallower water on a beach, they steepen until breaking occurs.
The energy of the waves is proportional to the square of the amplitude. Mathematical analysis shows that a distinction must be made between the speed of the troughs and crests, called the phase speed, and the speed and direction of the transport of energy or information associated with the wave, termed the group velocity. For nondispersive long waves the two are equal, whereas for surface gravity waves in deep water the group velocity is only half the phase speed. Thus, in a train of waves spreading out over a pond after a sudden disturbance at a point, the wave front travels at only half the speed of the crests, which appear to run through the packet of waves and disappear at the front. For capillary waves the group velocity is one and one-half times the phase speed.
Three types of water waves may be distinguished: wind waves and swell, wind surges, and sea waves of seismic origin (tsunamis). In addition, standing waves, or seiches, can occur in water bodies with enclosed or nearly enclosed basins, and internal waves, which appear as undulating layers of rapidly changing density with increasing depth, take plac...
Wind waves are the wind-generated gravity waves. After the wind has abated or shifted or the waves have migrated away from the wind field, such waves continue to propagate as swell.
The dependence of the sizes of the waves on the wind field is a complicated one. A general impression of this dependence is given by the descriptions of the various states of the sea corresponding to the scale of wind strengths known as the Beaufort scale, named after the British admiral Sir Francis Beaufort. He drafted it in 1808 using as his yardstick the surface of sail that a fully rigged warship of those days could carry in the various wind forces. When considering the descriptions of the sea surface, it must be remembered that the size of the waves depends not only on the strength of the wind but also on its duration and its fetch—i.e., the length of its path over the sea.
The theory of waves starts with the concept of simple waves, those forming a strictly periodic pattern with one wavelength and one wave period and propagating in one direction. Real waves, however, always have a more irregular appearance. They may be described as composite waves, in which a whole spectrum of wavelengths, or periods, is present and which have more or less diverging directions of propagation. In reporting observed wave heights and periods (or lengths) or in forecasting them, one height or one period is mentioned as the height or period, however, and some agreement is needed in order to guarantee uniformity of meaning. The height of simple waves means the elevation difference between the top of a crest and the bottom of a trough. The significant height, a characteristic height of irregular waves, is by convention the average of the highest one-third of the observed wave heights. Period, or wavelength, can be determined from the average of a number of observed time intervals between the passing of successive well-developed wave crests over a certain point, or of observed distances between them.
Wave period and wavelength are coupled by a simple relationship: wavelength equals wave period times wave speed, or L = TC, when L is wavelength, T is wave period, and C is wave speed.
The wave speed of surface gravity waves depends on the depth of water and on the wavelength, or period; the speed increases with increasing depth and increasing wavelength, or period. If the water is sufficiently deep, the wave speed is independent of water depth. This relationship of wave speed to wavelength and water depth (d) is given by the equations below. With g being the gravity acceleration (9.8 metres [about 32 feet] per second squared), C2 = gd when the wavelength is 20 times greater than the water depth (waves of this kind are called long gravity waves or shallow-water waves), and C2 = gL/2π when the wavelength is less than two times the water depth (such waves are called short waves or deepwater waves). For waves with lengths between 2 and 20 times the water depth, the wave speed is governed by a more-complicated equation combining these effects:
where tanh is the hyperbolic tangent.
Running wind surges are long waves caused by a piling up of the water over a large area through the action of a traveling wind or pressure field. Examples include the surge in front of a traveling storm cyclone, particularly the devastating hurricane surge caused by a tropical cyclone, and the surge occasionally caused by a wind convergence line, s...
A tsunami (Japanese: tsu, “harbour,” and nami, “wave”) is a very long wave of seismic origin that is caused by a submarine or coastal earthquake, landslide, or volcanic eruption. Such a wave may have a length of hundreds of kilometres and a period on the order of a quarter of an hour. It travels across the ocean at a tremendous speed. (Tsunamis are...
A freestanding wave may arise in an enclosed or nearly enclosed basin as a free swinging or sloshing of the whole water mass. Such a standing wave is also called a seiche, after the name given to the oscillating movements of the water of Lake Geneva, Switzerland, where this phenomenon first was studied rigorously. The period of oscillation is independent of the force that first brought the water mass out of equilibrium (and that is supposed to have ceased thereafter); it depends only on the dimensions of the enclosing basin and on the direction in which the water mass is swinging. Assuming a simple rectangular basin of constant depth and the most simple lengthwise oscillation, the period of oscillation (T) is equal to two times the length of the basin divided by the wave speed computed from the shallow-water formula above. This relationship may be written: T = L/C, in which L equals two times the length of the basin and C is the wave speed found from the formula, using the known depth of the basin. Besides this fundamental tone (or response to stimuli), the water mass also may swing according to an overtone, showing one or more nodal lines across the basin.
The water in an open bay or marginal sea also may perform such a free oscillation as a standing wave, the difference being that in an open bay the greatest horizontal displacements are not in the middle of the bay but at the mouth. For the fundamental period of oscillation, the formula given above is used with a wavelength equal to four times the length (from the mouth to the closed end) of the bay. In practice, of course, it is more difficult than that, because the form of a bay or marginal sea is irregular and the depth differs from place to place. The North Sea has a period of lengthwise swinging of about 36 hours. The cause of such free oscillations may be a temporary wind or pressure field, which brings the sea surface out of its horizontal position and which afterward ceases to act more or less abruptly, leaving the water mass out of equilibrium.
Gravity waves also occur on internal “surfaces” within oceans. These surfaces represent strata of rapidly changing water density with increasing depth, and the associated waves are called internal waves. Internal waves manifest themselves by a regular rising and sinking of the water layers around which they centre, whereas the height of the sea surface is hardly affected at all. Because the restoring force, excited by the internal deformation of the water layers of equal density, is much smaller than in the case of surface waves, internal waves are much slower than the latter. Given the same wavelength, the period is much longer (the movements of the water particles being much more sluggish), and the speed of propagation is much smaller; the formulas for the speed of surface waves include the acceleration of gravity, g, but those for internal waves include gravity multiplied by the difference between the densities of the upper and the lower water layer and divided by their average.
The cause of internal waves may lie in the action of tidal forces (the period then equaling the tidal period) or in the action of a wind or pressure fluctuation. Sometimes a ship may cause internal waves (dead water) if there is a shallow brackish upper layer.
Waves are, for the most part, formed from the transfer of wind energy along the surface of a water body. These are most commonly found in the ocean, but larger bodies of water, such as Lake Superior in North America, can form large waves due to wind and tidal activity.
When waves travel into areas of shallow water, they begin to be affected by the ocean bottom. [1] The free orbital motion of the water is disrupted, and water particles in orbital motion no longer return to their original position.
