2-Point Source Interference Patterns
Changing Separation Distance
Wave interference is a phenomenon which occurs when two waves meet while traveling along the same medium. Wave interference can be constructive or destructive. Constructive interference occurs at locations where the two interfering waves are displaced in the same direction - either both up or both down. When constructive interference occurs at a location along a medium, the resultant displacement of the medium at that location is larger than the displacement of either of the two individual waves. A new and larger wave is constructed. Destructive interference occurs at locations where the two interfering waves are displaced in the opposite direction - one wave is displaced up and the other displaced down. When destructive interference occurs at a location along the medium, the two individual waves combine to produce a new wave which has a resultant displacement which is smaller than the displacement of either wave at the location. That is, the two waves combine to either partially or completely destroy each other.
The interference of two sets of circular waves with the same frequency and the same amplitude results in a standing wave pattern. These standing wave patterns are known as two-point source interference patterns since they result from the interference of circular waves from two sources. A standing wave pattern is a wave pattern in which there are points along the medium which appear to be standing still. These points are called nodes - points of no displacement. Nodes are produced when destructive interference always occurs at the same location. Both waves have the same magnitude of displacement in opposite directions and interfere to provide complete destructive interference and no resulting displacement of the medium. In a standing wave pattern, the nodes are separated by antinodes. Antinodes are points along the medium which oscillate between a large negative displacement and a large positive displacement. Antinodes result from the constructive interference of two waves. At the antinodal positions, a crest meets a crest to produce a large positive displacement. Moments later, a trough meets a trough to produce a large negative displacement.
The diagram below shows several two-point source interference patterns. The crests of each wave is denoted by a thick line while the troughs are denoted by a thin line. Subsequently, the antinodes are the points where either the thick lines are meeting or the thin lines are meeting. The nodes are the points where a thick line meets a thin line.
Observe that the nodes of the pattern are oriented along lines - known as nodal lines. Similarly, the anti-nodes in the pattern are also oriented along lines - known as antinodal lines. The spacing between these lines is related to the distance between the sources. The two sources are represented by S1 and S2 in the diagram. As the sources move closer together, the spacing between the nodal lines and the antinodal lines increases. That is, the nodal and antinodal lines spread farther apart as the sources come closer together.
In 1801, Thomas Young used a two-point source interference pattern to measure the wavelength of light. Young passed sunlight through two slits (acting as the sources) and upon a screen some distance away. The projection of the nodal and anti-nodal lines on the screen produced an alternating pattern of dark and bright lines. Young used wave principles to establish that the wavelength of light could be mathematically related to the separation distance, the distance to the screen, and the distance between anti-nodal lines (bright spots). Young made accurate measurements and determined the wavelength of light.
For more information on physical descriptions of waves, visit The Physics Classroom Tutorial. Detailed information is available there on the following topics:
Two Point Source Interference
Anatomy of a Two-Point Source Interference Pattern
The Path Difference
Other Applications of Two Point Source Interference
Interference of Waves
Formation of Standing Waves
Nodes and Anti-nodes