What are the Characteristics of Two-Dimensional Waves?

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Two-dimensional waves are waves that have the ability to travel in more than one dimension. Such waves are those that can travel around corners. Examples of two-dimensional waves are sound waves and water waves. Two-dimensional waves can be illustrated on a ripple tank, which is a glass-bottomed water tank. Dark and light spots are experienced on white sheets of paper as rays of light bend after passing through crests and troughs (Goldberg). The bright spots represent wave crest, whereas the dark spots represent troughs. The wave’s behavior after meeting obstacles may be observed through the movements made by the bright and dark spots. Waves that originate from linear sources are straight, while those originating from point sources are circular. Wave properties such as frequency, wavelength, and velocity apply to two-dimensional waves. The wave equation also holds true for the waves. Two-dimensional waves have a wavefront and a wave ray that are usually perpendicular to each other at a point. A wavefront is the continuity of troughs and crests, while a wave ray signifies the direction of a wave.

An incoming wave ray is known as the incident ray, while an outgoing wave ray is known as the reflected ray. In the event that a wave strikes a barrier in a perpendicular position, it is reflected along the same path. On the contrary, a wave that hits a barrier at an angle is reflected at the same angle that it meets a surface. The representation for this is i=r, where r is the angle of reflection and i is the angle of incident. The representation i=r also applies to circular waves that meet straight barriers. The laws of reflection also apply when straight waves hit parabolic reflectors in such a case; they are reflected towards a focal point. Waves directed towards parabolic reflectors from a focal point result in straight waves.

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When two-dimensional waves pass through different mediums, they tend to change their direction of motion, which is known as refraction. The change in direction of a wave, or refraction, comes along with the change of the wavelength and speed of a wave. However, the frequency of the wave does not change. Water waves slow down when moving from deep to shallow water and increase in speed when moving from shallow to deep water. Refraction only occurs on the boundary of two mediums, only when the wave meets the other medium at an angle (Goldberg). Refraction does not occur when the wave meets a different medium at a straight line. In case the wave speed decreases after meeting a different medium, the refracted ray bends closer to the normal. On the other hand, if the speed increases, the ray bends away from the normal. The equation that relates to the angle of incident and the angle of refraction and the speed of the water wave on the two mediums is:

Sinβi /sinβr =V1 /V2 .
The equation expresses Snell’s Law. The index of refraction equals the ratio of the two speeds.
1n2 = V1 /V2 .
Sinβi /sinβr = 1n2

After passing around a barrier or through an opening, two-dimensional waves usually change their direction. Waves have the tendency of travelling through openings, around obstacles, and around corners. This is mostly common for water waves. This wave characteristic is known as diffraction. Diffraction in waves changes with the change of wavelength. Diffraction is more on longer wavelengths and less on shorter wavelengths. Finally, yet importantly, two-dimensional waves have a characteristic known as interference. In these types of waves, interference can be either destructive or constructive. In waves with the same frequency, amplitude, and wavelength, there are resultant nodes and antinodes and thus, interference is constructive.

  • Goldberg, Fred. Physical Science & Everyday Thinking. Armonk, New York: It’s About Time, Herff Jones Educational Division, 2009.

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