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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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Any two adjacent nodal positions are separated from each other by one-half a wavelength. See Know the Law section. So to determine the number of full wavelengths within the entire length of the rope, count the number of one-half wavelengths by beginning at one end and proceeding to the opposite end.
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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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