1. AP Physics
Section to 11-14
Wave Behavior

2. AP Physics Boundary behavior Wave Behavior Section 11-11 to 11-14
When a wave pulse or a continuous wave train hits a material of different density, it will be fully or partially reflected. The wave striking the boundary is the incident wave. On reflection, it becomes the reflected wave.
If the other medium can vibrate, the nature of the reflection depends on whether that medium is more or less dense than the original medium.

3. Pulses on a fixed boundary
When hitting a very dense medium, the wave is inverted on reflection.
Pulses on a soft (loose) boundary
When hitting a free-moving boundary, the wave is not inverted.

4. High to low density boundary
Example: water to air
Part of the wave will be reflected, and part transmitted to the low density medium.
What is true of the reflection?
Not inverted. Reduced in amplitude (energy).
What is true of the transmitted pulse?
Not inverted. Greater in amplitude.
Low to high density boundary
Example: air to water
What is true of the reflection?
Inverted. Reduced in amplitude (energy).
What is true of the transmitted pulse?
Not inverted. Lower in amplitude.

5. Superposition and interference
Principle of superposition — the displacement of a medium caused by two or more waves is equal to the algebraic sum of the displacements caused by the individual waves.
At one point, the wave displacements add as integers. If the signs are the same, the waves add together to make a larger amplitude. This is constructive interference.
Pulse interference

6. In this animation, two waves in the medium have the same amplitude, but the second is moving faster relative to the first. There will be periods of constructive and destructive interference.

7. Standing waves two in phase out of phase
When two waves traveling from opposite directions meet, a standing wave may form. The waves interfere to create the appearance of a wave with no motion.
two in phase
out of phase

8. Standing waves may be caused by a wave train reflecting from a boundary. The reflected wave interferes with the incident wave.
fixed boundary
soft boundary
If the boundary is in between, some energy is lost, and the reflected amplitude will be different. An impedance discontinuity is created.

9. Waves in two dimensions
Waves of course can propagate in two or three dimensions. Water waves in a pool or lake are a good example of a two dimensional wave.
The crests of the waves are called wave fronts.
An arrow representing the direction of motion of the wave front is called a ray.
It is always perpendicular to the wave front.
ray

10. Law of reflection θi = θr
The law of reflection states that the angle the incident wave makes with the normal to the surface will equal the angle of reflection.
Note that the angles are to the normal, not the surface.
θi = θr

11. Refraction
When a wave front moves at an angle into a medium of a different density, the wave front will bend and the speed will change.
Since the frequency of the wave remains constant, the wavelength changes with the speed.