Changes with respect to position
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a) Positions of the antinodes
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Consider the positions, where
Since the resultant amplitude R is maximum, these points correspond to the antinodes. It may be noted that the antinodes correspond to 
i.e., zero strain. Thus, antinodes are obtained at those points corresponding to
The antinodes are formed at those points corresponding to 
etc. The result that x = 0 corresponds to an antinode, indicates that the open end of an organ pipe or the free end of a stretched string corresponds to an antinode.
b) Positions of the nodes
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Consider the positions, where
Then y = 0
R = 0
Since y = 0, these positions correspond to nodes. The strain represented by
will be maximum at these points.
From the above analysis, it follows that two consecutive nodes or antinodes are separated by
l/2. A node and the adjacent antinodes are separated by
l/4. Between two nodes, an antinode is formed and vice versa.
Case (ii) Reflection occurring at a fixed end
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In this case, there will be a reversal of phase due to reflection. Let the incident wave be represented by the equation.
The reflected wave will have the same magnitude of the amplitude, velocity and wavelength. Due to reversal of phase (i.e., a crest returning as a trough or vice versa) the sign of A is reversed in the expression for y
2.
The resultant displacement of the particle subjected to these two displacements simultaneously, is
y = y1 + y2
Using the identity
This represents a simple harmonic wave whose amplitude has the magnitude
The velocity of the particle at any instant of time is given by
Acceleration is given by
The strain or the compression is given by
Changes with respect to position
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a) Positions of the antinodes
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Consider those positions where
Since the resultant amplitude is maximum, these points correspond to antinodes.
antinodes are obtained at points corresponding to
b) Positions of the nodes
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Consider the positions where
Then y = 0
R = 0
Since the resultant amplitude is zero, these positions correspond to nodes.
Therefore, the fixed end corresponds to a node.
