1. Finishing Chapter 3 and moving on to a music science diversion
Set - 5
Finishing Chapter 3 and moving on to a music science diversion

2. Hojadu?

3. How DID you do?? (We will ask again after the grades are back)
I did great
I did OK
Not so good
Bad
Very bad

4. How do you get your grade?
The cards must be processed.
The data will be downloaded to myUCF site.
NOT WebCT
NOT Blackboard
I may upload them to WebAssign as well. They have a gradebook function.
Probably about a week. Maybe already there!

5. What Happens Now?? We will complete some issues from Set-4
We move on to the first serious topics in the physical science of music.
Later we will return to the world of physics to pick up some more background.
Next week, as soon as I get them, I will review the exam and will post a concept list by question so you can know what concepts you need to review. Or not!

6. Let’s talk more about friction.
Stationary
Both forces the same
Stationary – Pushing harder. Both the same.
Moving
Push bigger than frictional force.

7. Graph
Stationary
Friction Newtons
Moving
Force Newtons

9. Applied force W f N

10. Frictional Force
Stationary Sliding
Applied Force

11. Friction

12. Which coefficient of friction is the largest?
Static
Dynamic
They are both the same.

13. The Violin – Friction in Motion!

14. The Bow
Horsehair

15. The Bowing Process of a Violin
Performer pushes down
And to the right
Motion of Bow
Frictional Force
Reaction Force
String on Bow
Focus in on the
relative motion of
the bow and the string

16. The Process Static Motion String moves with bow Still Static
Friction about
to change to
sliding friction
Sliding friction. The
string slips back due
to inertia until the string
pressure goes in the other
direction
Process repeats

17. Application ?? Physics Later

18. Things that go back and forth
Guitar Strings
Pendulum
Mass on Spring

19. The Spring

20. F=-kx Spring Force Equatiom
The “-” sign indicates that the force and the displacement are in opposite directions.

21. Springs Oscillate

22. Graph

23. Important Result for a Spring:

24. So ….

25. A string is just
a spring misspelled!

26. Concept … Tension

27. The Musical String Like a spring! Linitial T x T T
Force = F x T T
The Bigger the angle the
more T points UP!
The distance “x” is the same
sort of thing as the x in F=-kx.
ANGLE
Like a spring!

28. Spring /String Motion -1.5 -1 -0.5 0.5 1 1.5 5 10 15 20 25
0.5 1
1.5 5 10 15 20 25
Time (seconds)
disturbance
Height

29. The Guitar Strings

30. Stringed Instruments
PLUCK
Momentum

31. Important Definitions
The PERIOD, T is the time it takes to go from one condition to the next time that exact condition is repeated.
The frequency, the number of oscillations per second, is given by:
Example:
If T=2 seconds
F=1/2 (sec-1)=0.5 per second

32. Question
What is a tone and how
do you prove it??

33. Remember Helmholtz
In physiology and physiological psychology,
he is known for his mathematics of the eye,
theories of vision,
ideas on the visual perception of space,
color vision research,
the sensation of tone,
perception of sound.
In physics, he is known for his theories on the conservation of force,
work in electrodynamics, chemical thermodynamics,
A mechanical foundation of thermodynamics.

34. Helmholtz  Today
The SINE curve

35. Two Fuzzy Sine Waves

36. We Know (And will know even more later)
Tone

37. Today’s Approach

38. Speaker

39. Into the air …
Credit:

40. Helmholtz’s Results Note from Middle C Frequency C 264 D 297 E 330 F
352 G
396 A
440 B
496

41. We can study these tones with electronics
Or:

42. Oscilloscope

43. One More Tool
Tone
Signal Generator
Electrical

44. In using these modern tools
We postpone understanding how some of these tools work until later in the semester.
We must develop some kind of strategy to convince us that this approach is appropriate.

45. The Spring

46. F=-kx Spring Force Equatiom
The “-” sign indicates that the force and the displacement are in opposite directions.

47. Springs Oscillate

48. Graph

49. Important Result for a Spring:

50. So ….

51. A string is just
a spring misspelled!

52. Concept … Tension

53. The Musical String Like a spring! Linitial T x T T
Force = F x T T
The Bigger the angle the
more T points UP!
The distance “x” is the same
sort of thing as the x in F=-kx.
ANGLE
Like a spring!

54. Another piece of the string!
Lstretchl
Linitial F
Lfinal

55. The Guitar Strings

56. Consider Two Situations
For the same “x” the
restoring force is double
because the angle is
double.
The “mass” is about half
because we only have
half of the string
vibrating.

57. So… For the same “x” the restoring force is double
because the angle is
double.
The “mass” is about half
because we only have
half of the string
vibrating.
k doubles
m -> m/2
f doubles!

58. Guitar
Pressing the fret that is in the middle of the string doubles the frequency~
Walla … the octave
In general … the frequency is proportional to the length of the string.
Next time we will examine the monochord and Dr. Koons will show us how we develop (a) musical scale(s).

59. Now …. lets look at the MONOCHORD

60. HAVE FUN!

61. It has been shown that …
More about this when we do the string thing.

62. Octave