Interference & Superposition
The Physics Hypertextbook™
© 1998-2008 by Glenn Elert -- A Work in Progress
All Rights Reserved -- Fair Use Encouraged
Discussion
Discussion
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mention fourier
Summary
- Objects made of matter
- are material, tangible, corporeal, and definite
- cannot occupy the same place at the same time
- exchange energy and momentum during collisions
- Waves
- are immaterial, intangible, incorporeal, and indefinite
- can occupy the same place at the same time
- pass through each other without effect
- Principle of Linear Superposition
- When waves occupy the same place at the same time they interfere or superpose
- The resultant disturbance is the sum of the individual disturbances at every point in space and time
Problems
practice
- Write something.
- Answer it.
- Write something else.
- Answer it.
- Graph the following Fourier series with enough detail that you can determine basic shape of each wave.
y = Σ 1 sin(2n − 1)x = sin x + 1 sin 3x + 1 sin 5x + 1 sin 7x + 1 sin 9x + ⋯ 2n − 1 3 5 7 9 y = Σ (− 1)n +1 sin nx = sin x − 1 sin 2x + 1 sin 3x − 1 sin 4x + 1 sin 5x − ⋯ n 2 3 4 5 y = Σ 1 cos(2n − 1)x = cos x + 1 cos 3x + 1 cos 5x + 1 cos 7x + 1 cos 9x + ⋯ (2n − 1)2 9 25 49 81 Solutions …
- square wave
- sawtooth wave
- triangle wave
[image]
- Write something completely different.
- Answer it.
conceptual
- Walking involves the coordinated periodic motion of various parts of your
body. Identify the parts of your body that are moving …
- in phase with each other
- out of phase with each other
worksheets
- worksheet-superposition.pdf
These unusually shaped wave pulses are heading towards each other in a medium whose wave speed is one grid unit per second. Draw the resulting shape of the medium one, two, three, and four seconds later.
Resources
- active noise reduction
- Defence and Civil Institute of Environmental Medicine (DCIEM), Canadian Forces
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