1. Vibrations that carry energy from one place to another
WAVES
Vibrations that carry energy from one place to another

2. Types of Wave
Mechanical. Examples: slinky, rope, water, sound, & earthquake
Electromagnetic. Examples: light, radar, microwaves, radio, & x-rays

3. What Moves in a Wave? Energy can be transported over long distances
The medium in which the wave exists has only limited movement
Example: Ocean swells from distant storms
Path of each bit of water is ellipse

4. Periodic Wave Source is a continuous vibration
The vibration moves outward

5. Wave Basics - Vocabulary
Wavelength is distance from crest to crest or trough to trough
Amplitude is maximum height of a crest or depth of a trough relative to equilibrium level

6. Frequency and Period
Frequency, f, is number of crests (waves) that pass a given point per second
Period, T, is time for one full wave cycle to pass
T = 1/f f = 1/T (inverses or reciprocals)
Waves /second = seconds/wave = f T

7. Unit of Frequency Hertz (Hz) Second-1 same as 1/second or per second
Used to be “cycles per second”

8. Wave Velocity
Wave velocity,v, is the velocity at which any part of the wave moves
If wavelength = l, v = lf
Example: a wave has a wavelength of 10m and a frequency of 3Hz (three crests pass per second.) What is the velocity of the wave? Hint: Think of each full wave as a boxcar. What is the speed of the train?

9. v = lf l =v/f f = v/ l l lambda = wavelength f frequency
v is sometimes called velocity of propagation (speed wave moves in medium)

10. Example
A ocean wave travels from Hawaii at 10 meters/sec. Its frequency is 0.2 Hz. What is the wavelength?
l = v/f = 10/0.2 = 50 m

11. Second example
What is the wavelength of 100 MHz FM radio waves? Use v = c = 3 x 108 m/s
l = v/f = 3 x 108 m/s ÷ 100 x 106 s-1
= (300 x 106) ÷ (100 x 106) m
= 3.0 m

12. Another example
Waves travel 75 m/s on a certain stretched rope. The distance between adjacent crests is 5.0 m. Find the frequency and the period.
f = v/l
f = 75 m/s ÷ 5.0 m = 15 Hz = 15 s-1
T = 1/15 = s

13. Longitudinal vs. Transverse Waves
Transverse: particles of the medium move perpendicular to the motion of the wave
Longitudinal: vibrations in same direction as wave

14. Longitudinal Wave
Can be thought of as alternating compressions (squeezing) and expansions or rarefactions (unsqueezing)

15. Longitudinal Wave

16. Sound Wave in Air
Compressions and rarefactions of air produced by a vibrating object

17. Waves and Energy
Waves with large amplitude carry more energy than waves with small amplitude

18. Resonance
Occurs when driving frequency is close to natural frequency (all objects have natural frequencies at which they vibrate)
Tacoma Narrows bridge on the way to destruction– large amplitude oscillations in a windstorm

21. Interference
Amplitudes of waves in the same place at the same time add algebraically (principle of superposition)
Constructive interference:

22. Destructive Interference
Equal amplitudes(complete):
Unequal Amplitudes(partial):

23. Reflection Law of reflection:
Angle of Incidence equals angle of Reflection

24. Hard Reflection of a Pulse
Reflected pulse is inverted

25. Soft Reflection of a Pulse
Reflected pulse not inverted

26. Soft (free-end) Reflection

27. Standing Waves
Result from interference and reflection for the “right” frequency
Points of zero displacement - “nodes” (B)
Maximum displacement – antinodes (A)

28. Formation of Standing Waves
Two waves moving in opposite directions

29. Examples of Standing Waves
Transverse waves on a slinky
Strings of musical instrument
Organ pipes and wind instruments
Water waves due to tidal action

30. Standing Wave Patterns on a String
“Fundamental” =

31. First Harmonic or Fundamental

32. Second Harmonic

33. Third Harmonic

34. Wavelength vs. String length

35. String length = How many waves?
L = l

36. String length = How many waves?
L = 3/2 l

37. Wavelength vs. String Length
Wavelengths of first 4 harmonics
fl =v L

38. Frequencies are related by whole numbers
Example
f1 = 100 Hz fundamental
f2 = 200 Hz 2nd harmonic
f3 = 300 Hz 3rd harmonic
f4 = 400 Hz 4th harmonic
etc
Other frequencies exist but their amplitudes diminish quickly by destructive interference

39. Wave velocity on a string
Related only to properties of medium
Does not depend on frequency of wave
v2 = T/m/l Tension divided by mass per unit length of string

40. Standing Waves in Open Tubes

41. First Three Harmonics in Open Tube
Amplitudes are largest at the open ends
Amplitudes zero at the nodes

42. Tube Closed at One End f = vair/l L = l/4 L = 3l/4 L = 5l/4
No even harmonics present
f = vair/l

43. Beats Two waves of similar frequency interfere
Beat frequency equals the difference of the two interfering frequencies

44. Acknowledgements
Diagrams and animations courtesy of Tom Henderson, Glenbrook South High School, Illinois