A powerpoint detailing the aspects of resultant waves, superposition and interference. Provides a real life example with solutions.

1. SUPERPOSITION OF WAVES
Explanation and Real Life Application
Physics 101 - Learning Object

2. Superposition Principle
• Occurs when there is more than one wave in a medium at
a given time
• The Principle of Superposition states that a medium is
affected by each individual wave
- In other words, when more than one wave is present in a medium,
the waves do not have a influence on each other’s effect on the
medium

3. Superposition and Interference
• Resultant Wave (D)
- The sum of the individual waveforms of two or more waves within a
medium
- D(x, t) = D1(x,t) + D2(x,t) + D3(x,t) …
- In the figure below the black line, D(x, t), depicts the resultant wave
while the red and blue lines depict individual waveforms
- The resultant wave in the
figure is found by adding
together the D (m) of the
individual waveforms at
each position along the
wave

4. Superposition and Interference
• Superposition
- The formation of a resultant wave when two or more waves meet at
the same position, at the same time is known as superposition
• Interference
- Within the physical world the observation of superposition is known
as interference
- The interference of waves can be either constructive or destructive

5. Real Life Example
• Three children each drop a rock in the water at a distance
of 0.5m from one another at the same time. When each of
the rocks reach the water’s surface they generate their
own individual waveform. After a period of time these
waveforms coincide with one another and produce an
interference pattern similar to the one shown in the figure
below.

6. Real Life Example Questions
• Rock A produces a waveform with a displacement of 0.2m
• Rock B produces a waveform with a displacement of 0.4m
• Rock C produces a waveform with a displacement of 0.6m
For each of the individual waveforms a crest (maximum displacement)
is reached every 2m)
1. Sketch the position vs. displacement graphs for each of the
individual waveforms generated by the rocks
HINT: At x (position) = 0, the displacement of the rocks will be at their
maximum displacement

7. Question 1 Solution
• Rock A: Since the displacement in 0.2m and a crest is reached every
2m the position vs. displacement graph for the waveform of Rock A
would look as shown below:

8. Question 1 Solution
• Rock B: Since the displacement in 0.4m and a crest is reached every
2m the position vs. displacement graph for the waveform of Rock B
would look as shown below:

9. Question 1 Solution
• Rock C: Since the displacement in 0.6m and a crest is reached every
2m the position vs. displacement graph for the waveform of Rock C
would look as shown below:

10. Real Life Example Questions
2a. What will be the maximum and the minimum
displacements of the resultant wave?
2b. Will there be any points, along the interval of 0m to 4m,
where the displacement of the resultant wave is zero? If so,
at what positions would this occur?
HINT: To answer these questions, it may be helpful to
sketch the resultant wave’s position vs. displacement graph

11. Question 2 Solutions
• Resultant Wave Sketch: The position vs. displacement graph for the
resultant wave is determined by adding up the displacements of Rock
A, Rock B and Rock C at each position and then plotting them on the
graph

12. Question 2 Solutions
2a: Based on the resultant wave’s position vs. displacement graph it
can be determined that the maximum displacement is 1.2m and the
minimum displacement is -1.2m
• The maximum and minimum values can also be calculated without
the graph by adding together the maximum and minimum
displacements of each of the individual waveforms.
Ex. Maximum displacement (D) = 0.2 + 0.4 + 0.6 = 1.2
2b: Yes, there are places on the resultant wave where the
displacement is zero. As shown on the sketch of the position vs.
displacement graph for the resultant wave the displacement is zero at
x = 0.5, 1.5, 2.5, 3.5

13. Works Cited
• Water Interference
imagehttp://www.scienceclarified.com/photos/interference
-real-life-applications-3011.jpg