Because antinodes are vibrating back and forth between a large positive and large negative displacement, a diagram of a standing wave is sometimes depicted by drawing the shape of the medium at an instant in time and at an instant one-half vibrational cycle later. Antinodes are always vibrating back and forth between these points of large positive and large negative displacement this is because during a complete cycle of vibration, a crest will meet a crest and then one-half cycle later, a trough will meet a trough. Similarly, if a trough of one wave meets a trough of a second wave, a point of large negative displacement results. For instance, if a crest of one wave meets a crest of a second wave, a point of large positive displacement results.
Antinodes, on the other hand, are produced at locations where constructive interference occurs. For instance, nodes form at locations where a crest of one wave meets a trough of a second wave or a half-crest of one wave meets a half-trough of a second wave or a quarter-crest of one wave meets a quarter-trough of a second wave etc. The nodes are produced at locations where destructive interference occurs. The positioning of the nodes and antinodes in a standing wave pattern can be explained by focusing on the interference of the two waves. The finger is pointing at a nodal position. A strobe is used to illuminate the string several times during each cycle. It is this characteristic that has earned the pattern the name standing wave.Ī standing wave is established upon a vibrating string using a harmonic oscillator and a frequency generator. When a standing wave pattern is established in a medium, the nodes and the antinodes are always located at the same position along the medium they are standing still. The nodes and antinodes are labeled on the diagram. The animation shown below depicts a rope vibrating with a standing wave pattern. During any process, the net electric charge of an isolated system remains constant (i.e., conserved). e.g., if a body has different charges as +2q, +4q, + -3q, q, then total charge on the body is +2q. A standing wave pattern always consists of an alternating pattern of nodes and antinodes. Electric charge is additive (i.e., the total charge on a body is the algebraic sum of the charge present in different parts of the body). In a sense, these points are the opposite of nodes, and so they are called antinodes. These are the points that undergo the maximum displacement during each vibrational cycle of the standing wave. There are other points along the medium that undergo vibrations between a large positive and large negative displacement. These points, sometimes described as points of no displacement, are referred to as nodes. One characteristic of every standing wave pattern is that there are points along the medium that appear to be standing still.
A standing wave pattern is not actually a wave rather it is the pattern resulting from the presence of two waves of the same frequency with different directions of travel within the same medium. It is formed as the result of the perfectly timed interference of two waves passing through the same medium. As mentioned earlier in Lesson 4, a standing wave pattern is an interference phenomenon.
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