![]() ![]() A wavefront is the long edge that moves for example, the crest or the trough. The new wavefront is a line tangent to all of the wavelets.”įigure 17.4 shows how Huygens’s principle is applied. Huygens’s principle states, “Every point on a wavefront is a source of wavelets that spread out in the forward direction at the same speed as the wave itself. He used wavefronts, which are the points on a wave’s surface that share the same, constant phase (such as all the points that make up the crest of a water wave). The Dutch scientist Christiaan Huygens (1629–1695) developed a useful technique for determining in detail how and where waves propagate. Although wavelengths change while traveling from one medium to another, colors do not, since colors are associated with frequency. It follows that the wavelength of light is smaller in any medium than it is in vacuum. Where λ λ is the wavelength in vacuum and n is the medium’s index of refraction. As it is characteristic of wave behavior, interference is observed for water waves, sound waves, and light waves. Here we see the beam spreading out horizontally into a pattern of bright and dark regions that are caused by systematic constructive and destructive interference. Passing a pure, one-wavelength beam through vertical slits with a width close to the wavelength of the beam reveals the wave character of light. The laser beam emitted by the observatory represents ray behavior, as it travels in a straight line. In Figure 17.2, both the ray and wave characteristics of light can be seen. Interference is the identifying behavior of a wave. However, when it interacts with smaller objects, it displays its wave characteristics prominently. As is true for all waves, light travels in straight lines and acts like a ray when it interacts with objects several times as large as its wavelength. The range of visible wavelengths is approximately 380 to 750 nm. Earthquakes spread out, so they do less damage the farther they get from the source.Where c = 3.00 × 10 8 c = 3.00 × 10 8 m/s is the speed of light in vacuum, f is the frequency of the electromagnetic wave in Hz (or s –1), and λ λ is its wavelength in m. Sunlight, for example, can be focused to burn wood. ![]() Waves can also be concentrated or spread out. For example, the longer deep-heat ultrasound is applied, the more energy it transfers. ![]() The energy effects of a wave depend on time as well as amplitude. In fact, a wave’s energy is directly proportional to its amplitude squared because Because work \(W\) is related to force multiplied by distance (\(F_x\)) and energy is put into the wave by the work done to create it, the energy in a wave is related to amplitude. The larger the displacement \(x\) the larger the force \(F = kx\) needed to create it. More quantitatively, a wave is a displacement that is resisted by a restoring force. Large ocean breakers churn up the shore more than small ones. Loud sounds have higher pressure amplitudes and come from larger-amplitude source vibrations than soft sounds. Large-amplitude earthquakes produce large ground displacements. The amount of energy in a wave is related to its amplitude. (credit: Petty Officer 2nd Class Candice Villarreal, U.S. The Richter scale rating of earthquakes is related to both their amplitude and the energy they carry. \): The destructive effect of an earthquake is palpable evidence of the energy carried in these waves. ![]()
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