1. J. Pulickeel SPH3U1 January 2010
Waves At Boundaries 6.4:Transmission and Reflection 6.5: Waves in Two Dimensions
J. Pulickeel
SPH3U1
January 2010

2. Wave Behavior We know that waves travel through mediums.
What type of waves do not travel through a medium?
What types of waves travel through a medium?
Name 3 types of these waves
We know that waves travel through mediums.
But what happens when that medium runs out?

3. Boundary Behavior
The behavior of a wave when it reaches the end of its medium is called the wave’s BOUNDARY BEHAVIOR.
When one medium ends and another begins, that is called a boundary.

4. Fixed End
One type of boundary that a wave may encounter is that it may be attached to a fixed end.
In this case, the end of the medium will not be able to move.
What is going to happen if a wave pulse goes down this string and encounters the fixed end?

5. Fixed End Consider an incident pulse with an upward pulse.
What do you think will happen to the wave when it hits the anchor?
Click here for Phet Animation

6. Fixed End Animation
The reflected pulse is upside-down. It is inverted.
This is because of Newton’s Third Law. The wall is exert an equal in magnitude but opposite in direction force back on the string, thus causing the wave to return inverted.
The reflected pulse has the same speed, wavelength, and amplitude as the incident pulse.

7. Free End
Another boundary type is when a wave’s medium is attached to a stationary object as a free end.
In this situation, the end of the medium is allowed to slide up and down.
What would happen in this case?
If the end of an elastic rope is not fastened to the pole then it will be free to move up and down.

8. Free End Here the reflected pulse is not inverted.
It is identical to the incident pulse, except it is moving in the opposite direction.
The speed, wavelength, and amplitude are the same as the incident pulse.

9. Change in Medium
Consider a boundary condition where the medium of a wave changes.
Think of a thin rope attached to a thick rope. The point where the two ropes are attached is the boundary.
At this point, a wave pulse will transfer from one medium to another.
What will happen here?

10. Change in Medium
The denser material is somewhat like a fixed end because it will offer resistance to the wave motion. But it is like a free end also because it can move.
In this situation part of the wave is reflected, and part of the wave is transmitted.
Part of the wave energy is transferred to the more dense medium, and part is reflected.
The transmitted pulse is upright, while the reflected pulse is inverted.

11. The frequency remains the same!
Change in Medium
The speed and wavelength of the reflected wave remain the same, but the amplitude decreases.
The speed, wavelength, and amplitude of the transmitted pulse are all smaller than in the incident pulse.
The frequency remains the same!

12. Change in Medium Animation

13. Change in Medium Animation

14. Sound Travelling in the Same Medium
What will travel faster: A high frequency or a low frequency wave that is traveling in air?
Do you hear high frequency sounds faster than low frequency sounds? If you did, what would this mean about music?
Sound travels at the same speed in the same medium. A high frequency would have a low wavelength!
v = f λ

15. 6.5: Waves in 2D
We have only been considering waves in 1 dimension (eg. In a spring or rope).
Consider how waves move in 2 Dimensions
Parallel rays through a convex lense will bend towards the normal.
Parallel rays through a concave lense will bend away from the normal

17. Waves and Wave Fronts
Consider a wave travelling in the ocean. The wave ray (or incident wave) indicates the direction of transmission.
The wavefront is the leading edge of the wave. It is always ⊥ to the wave ray

18. Reflections of Waves
How would a light ray reflect off a plane boundary?
Reflecting surface
normal
Angle of Incident i
Angle of Reflection r
Incident ray
Reflected ray

19. Reflections of Waves
How would a light ray reflect off a plane boundary?
Reflecting surface
normal
Angle of Incident i
Wavefront
Angle of Reflection r
Reflected wave
Incident wave

20. Waves at a Parabolic Surface

21. Refraction and Diffraction
If a wave crosses the boundary at an angle, the direction of travel changes. This is called refraction.
Incident wave
Refracted wave

22. Refraction and Diffraction
if the wave passes by the sharp edge of an obstacle or through a small opening in the obstacle, the waves change direction. This bending is called diffraction.
Long-wavelength waves are diffracted more than short-wavelength waves. Decreasing the size of the opening will increase the amount of diffraction

23. Recall
What will happen to a wave when it travels into a denser medium? What is the difference between refraction and diffraction?
Draw the resulting wave front...