1. Vibrations and Waves

2. Vibrations and Waves “Wiggles in Time” “Wiggles in Space” Water Waves
Sound Waves
Light Waves
Oar in Water
Wings of a Bee
Electrons in an Light Bulb

3. Vibrations and Waves Waves transmit energy and information.
Sound and Light are both waves.

4. Simple Harmonic Motion...
…is to-and-fro vibratory motion.
...results in sine curves.
Examples:
metronome
mass on a spring
pendulum

5. Forces and vibrations Vibration - repetitive back and forth motion
At the equilibrium position, spring is not compressed
When disturbed from equilibrium position, restoring force acts toward equilibrium
Carried by inertia past equilibrium to other extreme
Example of “simple harmonic motion”

6. Describing vibrations
Amplitude - maximum extent of displacement from equilibrium
Cycle - one complete vibration
Period - time for one cycle
Frequency - number of cycles per second (units = hertz, Hz)
Period and frequency inversely related

7. Description Period - the time required for one vibration
measured in seconds
Frequency - number of vibrations per unit time
measured in Hertz
Bowling Ball Example

8. Bowling Ball Example

9. Pendulums & Galileo The period does not depend on the amount of mass.
The period does depend on the length of the pendulum.

10. * Example Test Question:
If you double the frequency of a vibrating object, what happens to the period?
a) the period doubles
b) the period stays the same
c) the period is cut in half d) not enough information is given
to answer this question.

11. Example Question *
Changing which of the following affects the period of a pendulum?
a) mass
b) amplitude
c) length
d) angle

12. What is the frequency in vibrations per second of a 60-Hz wave?
Answer: 60 cycles per second
What is its period?
Answer: 1/60 second

13. Waves Periodic (traveling) disturbances transporting energy Causes
Periodic motion disturbing surroundings
Pulse disturbance of short duration
Mechanical waves
Require medium for propagation
Waves move through medium
Medium remains in place

14. Wave Motion Waves Medium medium - the stuff that carries the wave
water waves
water
waves on a rope
rope
stadium waves
people
sound
air
light
space (vacuum)

15. Wave Speed... the speed with which waves pass by a particular point
e.g. the speed of a surfer
It depends only on the type of medium.
Wave Speed = Frequency  Wavelength
Waves on a Rope
Table in Notes – Appearance, Node, Antinodes, Wavelength, Frequency

16. Describing waves Graphical representation
Pure harmonic waves = sines or cosines
Wave terminology
Wavelength
Amplitude
Frequency
Period
Wave propagation speed

17. Example Test Questions Answer these questions using the sine wave provided.
What is the amplitude of the wave?
What is its wavelength?
How many nodes are there?

18. Example Wave
2 ½ meters
20 cm
Amplitude = 10 cm
Wavelength = 1 m
Number of Nodes = 6

19. If a water wave oscillated up and down three times each second and the distance between wave crest is 2 m, what is its frequency?
Answer: 3 Hz
What is its period?
Answer: 1/3 second
What is its wavelength?
Answer: 2 m
What is its wave speed?
Answer: 6 m/s

20. Kinds of waves, cont. Transverse waves
Vibration direction perpendicular to wave propagation direction
Example: plucked string
Solids - support both longitudinal and transverse waves
Surface water waves
Combination of both
Particle motion = circular

21. Kinds of waves Longitudinal waves
Vibration direction parallel to wave propagation direction
Particles in medium move closer together/farther apart
Example: sound waves
Gases and liquids - support only longitudinal waves

22. Waves in air Longitudinal waves only
Large scale - swinging door creates macroscopic currents
Small scale - tuning fork creates sound waves
Series of condensations (overpressures) and rarefactions (underpressures)

23. INTERFERENCE
Constructive or destructive interference results when waves add.
Standing Waves - wave pattern produced from interfering waves
Examples
Vibrating Strings in Lab
Organ Pipe in Lab
Bell Wave Machine in Class

24. http://www. kettering. edu/~drussell/Demos/superposition/superposition

25. DOPPLER EFFECT the change in wavelength due to motion of the source
"Wheeeeeeeeeeee…….Oooooooooooooo”
Examples:
moving cars and trains
moving buzzer in a nerf ball (in class)
rotating whistle
Draw Doppler Picture

26. Sounds from moving sources
Doppler effect
Wave pattern changed by motion of source or observer
Approaching - shifted to higher frequency
Receding - shifted to lower frequency
Supersonic speed - shock wave and sonic boom produced

28. Question 1 *
A train whistle at rest has a frequency of 3000 Hertz. If you are standing still and observe the frequency to be 3010 Hertz, then you can conclude that...
a) the train is moving away from you.
b) the train is moving toward you
c) the sound from the whistle has echoed
d) not enough information is given

29. Question 2 *
Dipping a finger in water faster and faster causes the wavelength of the spreading waves to
a) increase
b) decrease
c) stay the same
d) not enough information is given

30. Question 3 *
The distance from trough to trough on a periodic wave is called its...
a) frequency.
b) period.
c) wavelength.
d) amplitude.

31. Sound... ...a longitudinal wave in air caused by a vibrating object.
Sound requires a medium.
solid, liquid or gas
Sound waves have compression and rarefaction regions.

32. Nature of Sound in Air Sound requires a medium.
solid, liquid or gas
Demo: Bell in a evacuated Bell Jar
Sound waves have compression and rarefaction regions.

33. Sound infrasonic ultrasonic human hearing range frequencies < 20 Hz
frequencies between 20 Hz and 20,000 Hz

34. Sound waves Require medium for transmission Speed varies with
Inertia of molecules
Interaction strength
Temperature
Various speeds of sound

35. Velocity of sound in air
Varies with temperature
Warmer the air, greater the kinetic energy of the gas molecules
Molecules of warmer air transmit sound impulses from molecule to molecule more rapidly
Greater kinetic energy sound impulse transmitted faster
Increase factor (units!):
0.6 m/s/°C; 2.0 ft/s/°C

36. SPEED OF SOUND How it varies: increases with humidity
increases with temperature
increases with density

37. Lightning and Thunder

38. What is the approximate distance of a thunderstorm when you note a 3 second delay between the flash of the lightning and the sound of the thunder?
Answer: 3 seconds  340 meters/second
= 1020 meters
See blue questions on page 345. *

39. Sources of sound Vibrating objects Source of all sound
Irregular, chaotic vibration produces noise
Regular, controlled vibration can produce music
All sound is a combination of pure frequencies

40. Vibrating strings Important concepts - strings with fixed ends
More than one wave can be present at the same time
Waves reflected and inverted at end points
Interference occurs between incoming and reflected waves

41. Vibrating strings, cont.
Standing waves
Produced by interferences at resonant frequencies
Nodes - destructive interference points
Anti-nodes - points of constructive interference

42. Resonant frequencies of strings
Fundamental - lowest frequency
Higher modes - overtones (first, second, …)
Mixture of fundamental and overtones produces “sound quality” of instrument
Formula for resonant frequencies