1. What are waves?
A wave is a transfer of energy from one place to another.
Waves take many forms.
Wave Characteristics include:
Amplitude
Wavelength
Frequency
Period
Wave Speed

2. Transverse Waves
particles in the medium vibrate perpendicularly to the line of wave speed
Examples:
water waves,
waves on a string
wavelength
crest
amplitude
trough

3. Longitudinal Waves (Compressional Waves)
particles in the medium vibrate parallel to the wave velocity
made up of alternating areas of high pressure (compressions) and low pressure (rarefactions)
Examples: Sound waves, slinky waves
compression
rarefaction

4. Mechanical Waves Waves that require a medium to transfer energy.
May be either transverse or compressional (longitudinal).
Examples:
Sound waves, water waves, earthquake waves, waves in a string

5. Electromagnetic Waves
Waves that consist of an electric field and a magnetic field working to propagate it through free space (a vacuum)
No medium required
Best modeled using transverse waves
All EM waves travel at the speed of light, c c = 3 x 108 m/s
Examples:
light waves, microwaves, ultraviolet, infrared, radar, radio waves, gamma rays, x-rays, etc.

6. Wave Characteristics

7. Amplitude
Amplitude - the maximum displacement of the medium measured from the rest position.
Indicates the amount of energy carried by the wave
Crest - highest point on waveform, maximum displacement of medium
Trough - lowest point on waveform, maximum displacement of medium

8. Wavelength
The distance between corresponding points on consecutive waves.

9. Frequency
Frequency (f or n) - the number of complete cycles (waves) that pass a given point in the medium in 1 second. Measured in Hertz(Hz). 1 Hz = 1 cycle/sec.
stays the same when the wave goes from one medium to another

10. Period
Period (T) - the time it takes for one complete cycle to pass a given point in the medium, or the time that passes before the motion repeats itself. Measured in seconds.
f = 1/T T = 1/f

11. v = lf or v = ln Wave Speed velocity the wave travels through a medium
velocity is determined by the medium
v = lf or v = ln
“nu” - another symbol for frequency

12. Wave Behaviors

13. Reflection
Reflection is when wave changes directions because it encounters a barrier.
barrier
normal
Incident wave i
Reflected wave r
Law of Reflection: i = r
“Angle of incidence = Angle of reflection”

14. Refraction
Refraction occurs when a wave bends as is passes from one medium to another (crossing a boundary).
Medium determines wave speed and when wave speed changes, the wave bends.
water
normal
air
Incident wave
Boundary (water surface)
Refracted wave

15. Diffraction
The bending of waves around the edge of a barrier.

16. Boundaries
When a wave encounters the boundary between two media some will be reflected and some will be transmitted.
How much goes each way is determined by the relative densities of the media.
The transmitted pulses will always be erect (right side up)

17. Crossing Boundaries Less Dense to More Dense
When a wave is moving from a less dense medium to a more dense medium, the reflected pulse is inverted. v
Before
Less dense medium
More dense medium v
After v

18. Crossing Boundaries More Dense to Less Dense
When a wave is moving from a more dense medium to a less dense medium, the reflected pulse is erect. v
Before
More dense medium
Less dense medium v v
After

19. Interference
When two or more waves occupy the same space in a medium at the same time they interfere with each other.
The medium’s displacement will be the vector sum of the displacements caused by the individual waves.
After the waves pass each other they will return to their original forms.

20. Constructive Interference
When two waves interfere in a manner such that the amplitude of the resultant wave is greater than the amplitude of the individual waves.

21. Destructive Interference
When two waves interfere in a manner such that the amplitude of the resultant wave is smaller than the amplitude of the individual waves.
Note: Complete cancellation does not always occur in destructive interference.

22. Standing Waves
Caused by a wave and its reflected wave interfering in the medium
Wave pattern of alternating nodes and antinodes.
Nodes - areas of no displacement of the medium caused by destructive interference
Antinodes - areas of maximum displacement of the medium caused by constructive interference.
Note: The wavelength of a standing wave consists of 2 antinodes. 1 wavelength is shown.
node
Antinode