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Wave Interaction Help

By — McGraw-Hill Professional
Updated on Apr 25, 2014

Introduction

Two or more waves can combine to produce interesting effects and, in some cases, remarkable patterns. Amplitudes can be exaggerated, waveforms altered, and entirely new waves generated. Common wave-interaction phenomena include interference, diffraction , and heterodyning .

Interference

Imagine that you are a surfer. You spend the winter on the north shore of Oahu. In the maritime sub-Arctic, storms parade across the Pacific, spinning off from a parent vortex near the Kamchatka peninsula. You watch the satellite images of these storms on the Internet. The Kamchatka low is strong and stable, breeding systems that swoop southeastward and vent their fury in North America. Swells are propelled across the entire Pacific from these storms; there is nothing between the storm tracks and the shores of Hawaii. The swells arrive at places like Pipeline and break over coral and sand, reaching heights that often exceed 5 m (16 ft). Trade winds blow from east to west, producing smaller swells across the big ones. Gusts of wind and local squalls add chop. On a good day—the kind you, as a surfer, live for—the storm swell is strong, and the wind is light. You can ride the big breakers without being bumped around by the small stuff. On a bad day, waves pile onto waves in a haphazard way. The main swell is as big and well defined as on a good day, but the interference makes surfing difficult.

When two major marine storms are separated by a great distance, each producing significant swells, things get interesting. Such conditions are more likely to attract scientists than surfers. This type of situation can occur during the winter on the north shore of Oahu, but it is more often found in the tropics during hurricane season. Tropical storms produce some of the largest surf in the world. When a hurricane prowls the sea, swells radiate in expanding circles from the storm’s central vortex. If two storms of similar size and intensity are separated by a vast distance, complex swell patterns span millions of square kilometers. Between the storms, swells alternately cancel and reinforce each other, producing wild seas.

Interference patterns created by multiple wave sources appear at all scales, from swells at sea to sound waves in a concert hall, from radio broadcast towers to holographic apparatus. The slightest change in the relative positions or wavelengths of two sources can make a profound difference in the way the composite pattern emerges. Examples are shown in Figs. 17-4 and 17-5.

Wave Phenomena Wave Interaction Interference

Fig. 17-4 . A slight source displacement can change an interference pattern dramatically. Notice the difference between the pattern formed by the intersecting lines in part a , compared with the pattern in part b .

 

Wave Phenomena Wave Interaction Interference

Fig. 17-5 . Identical wavelength (a) versus a 10 percent difference (b) . Notice the difference in the interference pattern caused by the wavelength change.

Suppose that two tropical storms are sweeping around the Atlantic basin, steered by currents in the upper atmosphere. The interference pattern produced by their swells evolves from moment to moment. Multiple crests and troughs conspire along a front hundreds of kilometers long: a rogue wave . Such a monster wave can capsize ocean liners and freighters. Veteran sailors tell stories about walls of water that break in the open sea, seeming to defy the laws of hydrodynamics.

Wave interference on the high seas, while potentially frightening in its proportions, is not easy for scientists to observe. Patterns are sometimes seen from aircraft, and sophisticated radar can reveal subtleties of the surface, but oceans do not lend themselves to controlled experiments. Nor can you go out in a boat and sail into storm-swell interference patterns and expect to return with meaningful data, although you might end up with stories to tell your grandchildren if you survive. However, there are ways that even a child can conduct memorable experiments with wave convergence and interference.

Soap bubbles, with their rainbow-colored surfaces, are tailor made for this. Visible-light waves add and cancel across the visible spectrum, reflecting from the inner and outer surfaces of the soap film and teasing the eye with red, green, violet, then red again.

Adults can play with wave interference, too. Any building with a large rotunda provides a perfect venue. According to legend, long ago in the halls of Congress, a few elected officials were able to eavesdrop on certain supposedly private whisperings because the vast dome overhead reflected and focused the sound waves from one politician’s mouth to another’s ears.

Practice problems of these concepts can be found at: Wave Phenomena Practice Test

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