1. Vibrations and Waves
Chapter 11

2. Simple Harmonic Motion
Chapter 11 Section 1

3. Periodic Motion Any repetitive, or cyclical, types of motion
Examples?
Simple Harmonic Motion is a specialized form of periodic motion

4. Simple Harmonic Motion
Periodic vibration around an equilibrium position
Restoring force must be
proportional to displacement from equilibrium
in the direction of equilibrium

5. Restoring Force
The push or pull that brings the mass back towards equilibrium
The restoring force of a pendulum is a component of the bob’s weight.
The restoring force for a mass-spring system is from the stretch (or compression) of the spring

6. Simple Harmonic Motion
Common examples include a mass-spring system or a pendulum
For a pendulum, SHM only for small angles (within 10 degrees of vertical)

7. Describe speed, acceleration, and restoring force at each point.
Relaxed Length
Describe speed, acceleration, and restoring force at each point.

8. Describe speed, acceleration, and restoring force at each point.

9. Virtual Simple Harmonic Motion

10. Measuring Simple Harmonic Motion
Chapter 11 Section 2

11. Amplitude
The maximum displacement from equilibrium.

12. Period The time it takes for one complete cycle of motion.
Represented by the symbol T
Unit of seconds

13. Frequency
The number of cycles completed in a unit of time (usually seconds)
Represented by the symbol f
Unit of s-1 (also known as Hertz)

14. Period and Frequency f = 1/T and T = 1/f
Period and frequency are inversely related.
f = 1/T and T = 1/f

15. A mass spring system completes 10 cycles each second.
What is the period?
1/10 s
What is the frequency?
10 cycles per second (10 Hz)

16. Factors Affecting Pendulums
For small amplitudes, the period of a pendulum does not depend on the mass or amplitude.
Length does affect the period of a pendulum.

17. Factors Affecting Mass-Spring Systems
The heavier the mass, the longer the period (more inertia)
The stiffer the spring, the less time it will take to complete one cycle.

18. 11.2 Problems
Page 379 all
Page 381 all except for #3 on Section Review

19. Chapter 11 Section 3
Properties of Waves

20. Some general terminology…
Pulse – a single disturbance, single cycle
Periodic wave – continuous, repeated disturbances
Sine wave – a wave whose source vibrates with simple harmonic motion
Medium – whatever the
wave is traveling through

21. Wave Motion
A wave is the motion of energy away from a source of periodic disturbance.
Mechanical waves require a physical medium to travel through.
Examples: sound, disturbance in a slinky
Examples of physical media are water, air, string, slinky.

22. Electromagnetic waves
Do not require a physical medium.
Examples include x-rays, visible light, radio waves, etc.

23. Transverse Waves
Particles of the medium move perpendicular to the direction of energy transfer
You should be able to identify crests, troughs, wavelength (distance traveled during one full cycle), and amplitude
Crest
Trough

24. Longitudinal Waves
Particles of the medium move parallel to the direction of energy transfer (slinky demo)
Be able to Identify compressions, rarefactions, wavelengths
Compressions Rarefactions

25. Waves transfer energy
Note that, while energy is transferred from point A to point B, the particles in the medium do not move from A to B.
Individual particles of the medium merely vibrate back and forth in simple harmonic motion
The rate of energy transfer is proportional to the square of the amplitude
When amplitude is doubled, the energy carried increases by a factor of 4.

26. Wave speed
Wave speed is determined completely by the characteristics of the medium
For an unchanging medium, wave speed is constant
Calculate speed of a wave by multiplying wavelength by frequency.
v = f x λ

27. Practice #1
Q: Microwaves travel at the speed of light, 3.00108 m/s. When the frequency of microwaves is 9.00 109 Hz, what is their wavelength?
A: m

28. Practice #2
Q: The piano string tuned to middle C vibrates with a frequency of 264 Hz. Assuming the speed of sound in air is 343 m/s, find the wavelength of the sound waves produced by the string.
A: 1.30 m

29. 11.3 Problems
Page
Page

30. Wave Interactions
Chapter 11 Section 4

31. Interference
The combination of two or more waves in a medium at the same time.
Matter cannot occupy the same space at the same time, but energy can.
The Superposition Principle describes what happens when waves interfere…
Waves (energy) pass through each other completely unaffected
The medium will be displaced an amount equal to the vector sum of what the waves would have done individually

34. Constructive Interference
Waves are on the same side of equilibrium.
Waves meet, combine according to the superposition principle, and pass through unchanged.
Amplitude larger than originals

35. Destructive Interference
Waves are on the opposite sides of equilibrium.
Waves meet, combine according to the superposition principle, and pass through unchanged.
Amplitude smaller than at least one original wave

36. Complete Destructive Interference

37. Interference patterns
Interference patterns result from continuous interference.
Check it out!

38. Reflection
The bouncing of a wave when it encounters the boundary between two different media

39. Fixed End Reflection
At a fixed boundary, waves are inverted as they are reflected.

40. Free End Reflection
At a free boundary, waves are reflected on the same side of equilibrium

41. Standing Waves
A wave pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere.

42. Standing wave parts Node – point that maintains zero displacement
Antinode – point at which largest displacement occurs

43. Standing waves
Only certain frequencies produce standing wave patterns.

44. If a string is 4.0 m long, what are three wavelengths that will produce standing waves on this string?