Some Problems Musical Interlude – Stringed Instruments What do Springs Have To Do With It? 1.
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Transcript of Some Problems Musical Interlude – Stringed Instruments What do Springs Have To Do With It? 1.
Some Problems
Musical Interlude – Stringed Instruments
What do Springs Have To Do With It?
1
What are we doing???
• Today we finish up chapter 3,• Do some problems and• Move on to springs/music
• EXAM IS STILL APPROACHING!
2
Examination Date
Exam #1 Feb-11
Where are we??
3
aF
avv
vx
m
t
t
0
Let’s talk more about friction.
4
StationaryBoth forces the same
Stationary – Pushing harder. Both the same.
MovingPush bigger than frictional force.
Graph
5
Force Newtons
Fric
tion N
ew
tons
Stationary
Moving
6
7
Applied force
f
N
W
8
Applied Force
Stationary Sliding
Fric
tional Fo
rce
Friction
9
NF
Moving
NF
Static
d
s
Dynamic -
Which coefficient of friction is the largest?
A. StaticB. DynamicC. They are both the same.
10
The Violin – Friction in Motion!
11
The Bow
12
Horsehair
The Bowing Process of a Violin
13
Performer pushes downAnd to the right
Reaction ForceString on Bow
Motion of Bow
Frictional Force
Focus in on therelative motion of
the bow and the string
The Process
14
Static MotionString moves withbow
Still StaticFriction aboutto change tosliding friction
Sliding friction. Thestring slips back dueto inertia until the stringpressure goes in the otherdirection
Process repeats
APPLICATION ?? PHYSICS LATER
15
Things that go back and forth
• Pendulum• Mass on Spring
16
Guitar Strings
The Spring
17
Spring Force Equatiom
• F=-kx
• The “-” sign indicates that the force and the displacement are in opposite directions.
18
Springs Oscillate
19
Graph
20
21
Important Result for a Spring:
m
kf
kxF
2
1
So ….m
kf
2
1
22
23
Concept … Tension
24
The Musical String
25
Force = F
x
Linitial T
T TThe Bigger the angle themore T points UP!
The distance “x” is the samesort of thing as the x in F=-kx.
ANGLE
Spring /String Motion
26
-1.5
-1
-0.5
0
0.5
1
1.5
0 5 10 15 20 25
Time (seconds)
dis
turb
an
ce H
eig
ht
The Guitar Strings
27
Stringed Instruments
28
PLUCK
Momentum
Important Definitions
29
Tf
or
periodfrequency
1
1
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
Question
30
What is a tone and how do you prove it??
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.
31
1821 - 1894
32
Helmholtz Today
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12
Time in milli-seconds
"air
spee
d"
- re
lati
ve
The SINE curve
Two Fuzzy Sine Waves
33
34
We Know (And will know even more later)
Tone
Today’s Approach
35
Speaker
36
Into the air …
37Credit: http://www.soundonmind.com/
Helmholtz’s ResultsNote from Middle C Frequency
C 264
D 297
E 330
F 352
G 396
A 440
B 496
38
39
We can study these tones with electronics
Tone
Or:
Oscilloscope
40
http://commons.wikimedia.org/wiki/Main_Page
One More Tool
41
Tone
Signal GeneratorElectrical
In using these modern tools
1. We postpone understanding how some of these tools work until later in the semester.
2. We must develop some kind of strategy to convince us that this approach is appropriate.
42
Another piece of the string!
43
LinitialLstretchl
Lfinal
F
The Guitar Strings
44
Consider Two Situations
45
For the same “x” therestoring force is doublebecause the angle is double.
The “mass” is about halfbecause we only havehalf of the stringvibrating.
So…
m
kf
kxF
2
1
46
For the same “x” therestoring force is doublebecause the angle is double.
The “mass” is about halfbecause we only havehalf of the stringvibrating.
k doubles
m -> m/2
f doubles!
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).
47
Now …. lets look at the MONOCHORD
48
HAVE FUN!
49
It has been shown that …
k""constant spring a like Looks
area sectional-cross theisA
material afor constant a is E
withpullyou force theis F
initial
stretchinitial
L
EA
LL
EAF
50
More about this when we do the string thing.
Octave
51
0.001 0.002 0.003 0.004 0.005
-1
-0.5
0.5
1
0.001 0.002 0.003 0.004 0.005
-1
-0.5
0.5
1
0.001 0.002 0.003 0.004 0.005
-1.5
-1
-0.5
0.5
1
1.5