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Analysis of a Standing Wave Pattern:
A standing wave pattern shows a unique relationship between the wavelength of the waves that create the pattern and a length measured along the medium between two points on the pattern. Every nodal position on the pattern is separated from the next adjacent nodal position by one-half of a wavelength. Similarly, every antinodal position on the pattern is separated from the next adjacent antinodal position by one-half of a wavelength.
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The diagram of the standing wave pattern shows a collection of nodes and antinodes with the nodes being present on the ends. As mentioned in the Know the Law section, the nodes are separated by one-half of a wavelength. Start on the left end and count the number of one-half wavelengths which are in the entire length of rope. Then write an equation in which you express the relationship between the length (L) of the rope and the number of one-half wavelengths. For example, L = 7•(1/2•λ). Substitute the value of λ into your equation and solve for the length of the rope.
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The diagram shows the pattern made by the medium at two instants in time during a complete wave cycle. This is a very common way of representing a wave pattern. The pattern is drawn when the antinodal positions are at their maximum displacement from the resting position. And the mirror image is drawn to represent the pattern formed one-half period later when the antinodal positions have reached a maximum displacement in the opposite direction.
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