1. Vibrations and Waves

2. Good Vibrations!

3. At the heart of every wave
Do the moving vibration walking demo
Is a vibration.
All waves begin with a vibration
A vibration is a wiggle in space; something wiggles in time but does go anywhere.
A wave is a wiggle that goes somewhere; it is a wiggle in both time and space

4. Wave Motion A wave is the motion of a disturbance
Mechanical waves require
Some source of disturbance (a vibration)
A medium that can be disturbed
All waves carry energy and momentum
Not all waves are mechanical.

5. Types of Waves – Transverse
In a transverse wave, each element that is disturbed moves in a direction perpendicular to the wave motion

6. Types of Waves – Longitudinal
In a longitudinal wave, the elements of the medium undergo displacements parallel to the motion of the wave
A longitudinal wave is also called a compression wave

7. Amplitude of a Vibration
A = Δx
Symbol: A
Formula: A = ±Δx

8. Amplitude
Amplitude, A, is the distance from the most extreme point to the equilibrium point.
Amplitude is a length, so it is measured in meters

9. Period
Period, T, is the time it takes to get through one complete cycle - for example, through all the positions shown here.
The unit of period is a second

10. Frequency
Frequency, f, is the number of complete cycles an object completes in a second.
The unit for frequency is cycles/second, or “Hertz” (Hz)

11. Frequency and Period Frequency is the # of cycles per second
Period is the # of seconds per cycles
Notice: they are reciprocals of each other
f = 1/T
T = 1/f

12. Wave Speed
Remember that the “normal” speed, or velocity, equation is
v = d/t
And for waves, the speed still has the symbol v
For distance, we’ll use the length of one wave, λ
For time, we’ll use the period, T

13. Wavespeed, continued v = λf v = λ/T
Old style
Wave style
Speed, v
Wavespeed, v
Distance, d
Wavelength, λ
Time, t
Equation: v=d/t
Period, T
Equation: v = λ/T
V=λ/T which is the same as v=λ(1/T) but (1/T) = f, therefore
v = λf
v = λ/T

14. Traveling Waves Try this! Use a snakey spring.
Explore: the shape of the wave when it reflects
Explore: the speed of the wave – what can make it change?
Flip one end of a long rope that is under tension and fixed at one end
The pulse travels to the right with a definite speed
A disturbance of this type – where one-half a wave to a few waves travels along -- is called a traveling wave

15. Tsunami Feb 27, 2010 Website for Hilo footage – Feb 27, 2010
Thailand footage, 2006 (2.5 million deaths)

16. Standing Wave
There are 3 nodes and 2 antinodes in the photo
A standing wave has nodes (no amplitude) and antinodes (full amplitude)

17. Waveform – A Picture of a Wave
The brown curve is a “snapshot” of the wave at some instant in time
The blue curve is later in time
The high points are crests of the wave
The low points are troughs of the wave

18. Longitudinal Wave Represented as a Sine Curve
A longitudinal wave can also be represented as a sine curve
Compressions correspond to crests and stretches correspond to troughs
Also called density waves or pressure waves

19. Description of a Wave
A steady stream of pulses on a very long string produces a continuous wave
The blade oscillates in simple harmonic motion
Each small segment of the string, such as P, oscillates with simple harmonic motion

20. Amplitude and Wavelength
Amplitude is the maximum displacement of string above the equilibrium position
Wavelength, , is the distance between two successive points that behave identically

21. Speed of a Wave
v = ƒ 
Is derived from the basic speed equation of distance/time
This is a general equation that can be applied to many types of waves

22. Interference of Waves
Two traveling waves can meet and pass through each other without being destroyed or even altered
Waves obey the Superposition Principle
If two or more traveling waves are moving through a medium, the resulting wave is found by adding together the displacements of the individual waves point by point
Actually only true for waves with small amplitudes

23. Constructive Interference
Two waves, a and b, have the same frequency and amplitude
Are in phase
The combined wave, c, has the same frequency and a greater amplitude
Show Physlet

25. Constructive Interference in a String
Two pulses are traveling in opposite directions
The net displacement when they overlap is the sum of the displacements of the pulses
Note that the pulses are unchanged after the interference

26. Destructive Interference
Two waves, a and b, have the same amplitude and frequency
They are 180° out of phase
When they combine, the waveforms cancel

27. Destructive Interference in a String
Two pulses are traveling in opposite directions
The net displacement when they overlap is decreased since the displacements of the pulses subtract
Note that the pulses are unchanged after the interference

28. Wave Superimposition Animation
zonalandeducation.com/.webloc

29. Reflection of Waves – Fixed End
Whenever a traveling wave reaches a boundary, some or all of the wave is reflected
When it is reflected from a fixed end, the wave is inverted
The shape remains the same

30. Reflected Wave – Free End
When a traveling wave reaches a boundary, all or part of it is reflected
When reflected from a free end, the pulse is not inverted

31. Resonance - a special instance of constructive interference
Almost everything has a natural frequency
This is the frequency at which an object “wants” to vibrate
If you cause an item to vibrate at its natural frequency, the vibrations will add together
Demo: singing rod, standing wave in a string
Application: microwave oven, swings

32. Reflection angle
The angle of incidence is equal to the angle of reflection
Pass out mirrors to verify this!

33. For Honors students: θi = θr
Notice that the incident and reflected angles are measured from the normal

35. Refraction

36. Refraction Waves don’t always travel in straight lines.
When they bend due to a change in speed, we call this refraction

38. Diffraction
When a wave bends around a boundary, it’s called diffraction