1. Types, characteristics, properties
Waves
Types, characteristics, properties

2. Wave: definition
A quantity or disturbance that changes in magnitude with respect to time at a given location
Also changes in magnitude from place to place at a given time
Propagates through a medium or space
Transfers energy, not matter
water wave, sound, light, x-ray, earthquake

3. Wave Classification Schemes
Is medium needed for propagation?
Mechanical
Electromagnetic
How do particles move compared to motion of wavefront?
Transverse
Longitudinal

4. Mechanical Waves Require elastic medium for propagation
Energy source vibrates particles of medium about an equilibrium position
Each particle exerts force on adjacent particles passing energy along
Inertia of particles slows propagation of wave: wave speed depends on medium

5. Mechanical Waves
Particles move in SHM if wave train is generated by periodic motion
Examples: water waves, sound waves, earthquake waves, vibrating strings

6. Electromagnetic Waves
Self-propagating--need no medium for propagation
Can travel through vacuum of space
Examples: light waves, microwaves, x-rays, radio & TV broadcasts

7. Transverse Waves
Displacement of particles is perpendicular to direction of wave travel
crest: point of max. positive displacement
trough: point of max. negative displacement
examples: water, light, string, all electromagnetic waves

8. Longitudinal Waves
Displacement of particles is parallel to direction of wave travel
Series of high and low pressure areas in medium
Compression: high pressure area (like crest)
Rarefaction: low pressure area (like trough)
Ex: sound, Slinky, some earthquake waves

9. Characteristics of All Waves
Energy: waves transport energy
Phase: relative position between waves
Frequency: how many waves per second
Period: how long a time for one wave
Wavelength: distance between waves
Speed: how fast wave travels
Amplitude: how big the wave is

10. Wave Energy Depends on amplitude, frequency, and density of medium
Power (energy/time) is proportional to square of amplitude and/or frequency
With no losses to system, each wave has same energy as source
As wave moves outward, energy spreads over larger area, reducing amplitude

11. Phase
In phase: waves (or particles) are moving together, peaks line up with peaks and troughs line up with troughs
Out of phase: waves (or particles) are not aligned; totally out of phase, peaks line up with troughs, troughs with peaks
Phase relationship can be expressed in degrees, related to circular motion

12. Frequency number of wave pulses passing a point in a given time
Measured from identical points on successive waves
Symbol is f (or occasionally n (nu))
Unit is hertz (Hz), has SI units of sec-1
Old unit is cycles per second

13. Period Time for one wave cycle Symbol is T
Reciprocal of frequency T= 1/f

14. Wavelength Distance between identical points on successive waves
Also distance wave travels in one period
Measured in meters (or parts of meters)
Symbol is l (lambda)

15. Wave Speed Same as any speed: distance/time, symbol v, units m/s
Depends on medium and often on l
When speed depends on l in medium, medium is called dispersive
Causes dispersion, or spreading of wave according to wavelength; ex: rainbow
v = l / T = fl

16. Amplitude
In transverse wave, equals maximum displacement from equilibrium position
In longitudinal wave, equals maximum pressure change from normal pressure
Damping by dissipative forces reduces amplitude as wave travels

17. Wave Properties Rectilinear Propagation Reflection Impedance
Refraction
Diffraction
Interference

18. Rectilinear Propagation
In uniform medium, waves travel in straight lines, perpendicular to wavefront
Wave velocity direction also perpendicular to wavefront

19. Reflection Occurs at boundary between two media
Wave is returned to original medium
Can be partial or complete depending on how new media transmits wave energy
The more wave speed changes at media boundary, the more wave is reflected
Law of reflection: angle of incidence equals angle of reflection

20. Law of Reflection

21. Impedance A measure of how easily a wave can be produced in a medium
Equals ratio of applied force producing wave to resulting displacement velocity
If impedances of two media match, wave is not reflected and is transmitted with no loss
Impedance matching using transformers important for energy transmission systems

22. Impedance and Reflection
If wave can’t create displacement in particles of new media, impedance is infinite, wave is reflected out of phase: fixed end reflection
If wave producing force can’t be transferred to new media, impedance is zero and wave is reflected in phase: free end reflection

23. Refraction Bending of wave path at boundary between media
Due to different wave speed in new medium
Wave must strike boundary obliquely
Since v = fl , change in speed changes l
If v in new media < v in old media, wave bends towards normal of boundary & vice versa

24. Refraction

25. Wave speed increases

26. Refraction Applet

27. Diffraction
Spreading of wave beyond edges of barrier or past small opening
Causes bending of wavefront
Opening must be approximately same size as wavelength to diffract
Example: sound waves diffracted by doorways, light waves aren’t

28. Diffraction

29. Superposition Principle
When two or more waves travel through the same space (medium) at the same time . . .
Each wave proceeds independently as though no other waves were present
The resultant displacement of any particle is the vector sum of displacements each wave would give it alone.
Produces complex waveforms

30. Interference
Effects due to two or more superposed waves of similar frequency
If 2 waves of same type and frequency are in phase, displacements add, creating greater amplitude -- constructive interference
Same waves out of phase, resultant displacement is now difference, decreasing amplitude --destructive interference

31. Interference Patterns
Often destructive and constructive interference happens in different places at same time, creates interference pattern
Points of zero displacement, complete cancellation are called nodes
Points of max displacement called antinodes
Total wave energy doesn’t change, just rearranged

32. Standing Waves
Standing wave: produced by interference of 2 periodic waves of same amplitude and wavelength traveling in opposite directions
Usually wave reflected onto itself
Nodes remain stationary, energy remains standing at antinodes
Basis for all string and wind instruments