2-Point
Source Interference Patterns
Changing
Separation Distance
A GIF
Animation
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 wherever a crest of one wave meets a crest of
a second wave (or when a trough of two waves meet). When a crest meets a crest,
the resultant displacement of the medium at that location is larger than the
displacement of either of the two individual wave crests. A new and larger wave
is constructed. Destructive interference occurs wherever a crest of one wave
meets a trough of a second wave. When a crest meets a trough, the two
individual waves combine to produce a new wave which has a resultant
displacement which is smaller than the displacement of the larger wave. 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; a crest and a trough with the same magnitude of displacement
interfere to provide complete destructive interference and no resulting
displacement of the medium. In a standing wave pattern, the nodes are separated
by anti-nodes. Anti-nodes are points along the medium which oscillate between a
large negative displacement and a large positive displacement. Anti-nodes
result from the constructive interference of two waves. A crest meets a crest
to produce a large positive displacement; and moments later, a trough meets a
trough to produce a large negative displacment.
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 anti-nodes 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 anti-nodal 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 anti-nodal lines increases. That is,
the nodal and anti-nodal 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 monochromatic light 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.
