1. Properties of Waves

2. Wave Motion The medium is what a wave or disturbance travels through
Molecules vibrate up and down as the wave passes through
The medium does not actually travel with the waves
After a wave passes, the medium returns to its original position

3. Diagram of Wave
Have you ever "done the wave" as part of a large crowd at a football or baseball game? A group of people jumps up and sits back down, some nearby people see them and they jump up, some people further away follow suit and pretty soon you have a wave travelling around the stadium. The wave is the disturbance (people jumping up and sitting back down), and it travels around the stadium. However, none of the individual people the stadium are carried around with the wave as it travels - they all remain at their seats. Longitudinal sound waves in air behave in much the same way. As the wave passes through, the particles in the air oscillate back and forth about their equilibrium positions but it is the disturbance which travels, not the individual particles in the medium. Transverse waves on a string are another example. The string is displaced up and down as the wave travels from left to right, but the string itself does not experience any net motion

4. Nomenclature A - Amplitude - the maximum displacement from equilibrium
 - Wavelength - Distance between any two successive identical points.
f - Frequency - Number of cycles or oscillations per second. ( = 1/T)
T - Period - Time to complete one full oscillation or cycle. (=1/f)
Speed= frequency x wavelength

5. Parts of a Wave Crest: The highest point on the wave
Trough: The lowest point on the wave

6. Simple Harmonic Motion
A wave whose source vibrates with simple harmonic motion is called a sine wave
It is called a sine wave because a graph of the trigonometric function y=sine x produces this curve when plotted

7. Plot of Amplitude vs. Position

8. Mechanical Waves
Waves that require a medium are called mechanical waves
Sound requires air or water to travel
Light does not need a medium. It can travel through a vacuum.

9. Types of mechanical waves
Transverse – vibrations of wave are perpendicular () to direction of wave motion
Longitudinal – When the particles of a medium vibrate parallel () to direction of wave motion. Sound waves in air are longitudinal because air particles vibrate back and forth in a direction parallel to the wave motion
Pulse- a wave that consists of a single traveling pulse wave
Periodic- when you have more than one wave
Harmonic

10. One, Two, & Three Dimensions
One Dimension
Spring / Slinky
Two Dimension
Ripples on water
Three Dimension
Sound / Earth Quake

11. Pulse wave
A single oscillation sent through a media due to a non-repeating event.
e.g. Sound from an explosion or crash. Splash from a stone dropped in water.

12. Periodic Wave
Wave produced by an oscillation of the media which repeats with a regular period.
e.g. Sound from a steady drum beat

13. Harmonic (Standing) Wave
Created by a simple harmonic oscillations of the media.
Standing waves have nodes and antinodes
The resultant wave pattern does not move along the string
The points at which the two waves cancel each other are called nodes
Where the string vibrates with the larges amplitude is called the antinode.

14. Calculating Speed of a Wave
v = f 
Speed= frequency x wavelength

15. Different types of waves

16. Wave Interactions
Two different material objects can never occupy the same space at the same time.
When two waves come together they do not bounce back as bumper boats.
Because mechanical waves are not matter but rather the displacement of matter, who waves can occupy the same space at the same time

17. Displacement
The combination of two overlapping waves is called superpositon.
Displacement in the same direction produce constructive interference.
When two waves are added together the resultant wave is larger than the individual displacements and this is constructive interference.

18. Destructive Interference
Displacements in opposite directions produce destructive interference.
When positive and negative displacements are added, the resultant wave is the difference between the pulses, this is called destructive interference.

19. Reflection of Waves
At a free boundary, waves are reflected but not inverted
At a fixed boundary, waves are reflected and inverted

20. Wave reflection

21. Reflection of a wave from a free end
Animations courtesy of Paul Hewitt
and borrowed from physicsclassroom.com

22. Reflection of a wave from a fixed end
Animations courtesy of Paul Hewitt
and borrowed from physicsclassroom.com

23. Transmission
When a wave hits a surface or interface not all of the energy is reflected. Some is transmitted into the next medium.
The transmitted wave is “non-inverted” and the “harder” the surface the less is transmitted.

24. Travel between media of different density
Animations courtesy of Paul Hewitt
and borrowed from physicsclassroom.com

25. Longitudinal Wave Animations courtesy of Paul Hewitt
and borrowed from physicsclassroom.com

26. Standing Waves
Created by the interference of two waves of the same frequency traveling in opposite directions.
In a string or tube of limited length the reflections off the ends will create two traveling waves moving in opposite directions.
Only certain wavelengths () will create standing waves in a string or tube of limited length .
These wavelengths () correspond to frequencies (f = v/ ) called natural or resonant frequencies

27. Traveling Wave Animations courtesy of Paul Hewitt
and borrowed from physicsclassroom.com

28. Standing Wave Animations courtesy of Paul Hewitt
and borrowed from physicsclassroom.com

29. Fundamental Frequency
Animations courtesy of Paul Hewitt
and borrowed from physicsclassroom.com

30. Second Harmonic Animations courtesy of Paul Hewitt
and borrowed from physicsclassroom.com

31. Third Harmonic Animations courtesy of Paul Hewitt
and borrowed from physicsclassroom.com

32. Fourth Harmonic Animations courtesy of Paul Hewitt
and borrowed from physicsclassroom.com

33. Fifth Harmonic Animations courtesy of Paul Hewitt
and borrowed from physicsclassroom.com

34. Harmonics