1. Interference

2. Superposition
When two or more waves are present at the same time they add together.
Includes different frequencies
Includes different wavenumbers
When waves are added at each point to form a new quantity, they are said to be in superposition.

3. Constructive Interference
As pulses reach the same spot they add directly.
At later times they still add.
When two waves make a larger wave they have constructive interference.

4. Destructive Interference
Waves in the opposite direction can cancel each other out.
The waves still separately exist and may be moving.
This is called destructive interference.

5. Ripples
Wave on the surface of water have both constructive and destructive interference.
Gaps where the ripples cross are from the destructive intereference.

6. Building a Square Any wave form is the sum of harmonic waves.
One can construct a sequence of harmonic waves to match other shapes.

7. Obstacles
Small wavelength waves that encounter a large object leave a shadow area behind the object.
Large wavelength waves that encounter an object leave less shadow area.
This is called diffraction.

8. Bouncing Wave The medium for waves is not always uniform.
Collision with a barrier
A single pulse is reflected back in the opposite direction.

9. Open Ended The medium may end in air.
Extreme case the end is loose and completely free
A single pulse is reflected back in the same direction.

10. Standing Wave
When a wave reflects it sends the same frequency back again.
There are two waves of the same frequency moving in opposite directions.
This forms a standing wave.