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 ExaminationDate Exam #1 Feb-11
Where are we?? 3
Let’s talk more about friction. 4 Stationary Both forces the same Stationary – Pushing harder. Both the same. Moving Push bigger than frictional force.
Graph 5 Force Newtons Friction Newtons Stationary Moving
6
7 Applied force f N W
8 Applied Force Stationary Sliding Frictional Force
Friction 9
Which coefficient of friction is the largest? A.Static B.Dynamic C.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 down And to the right Reaction Force String on Bow Motion of Bow Frictional Force Focus in on the relative motion of the bow and the string
The Process 14 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
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:
So …. 22
23
Concept … Tension 24
The Musical String 25 Force = F x L initial T 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
Spring /String Motion Time (seconds) disturbance Height
The Guitar Strings 27
Stringed Instruments 28 PLUCK Momentum
Important Definitions 29 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,physiologyphysiological psychology he is known for his mathematics of the eye,eye theories of vision,vision ideas on the visual perception of space,perception color vision research, color vision the sensation of tone, perception of sound. In physics, he is known for his theories on the conservation of force,physicsforce work in electrodynamics, chemical thermodynamics,electrodynamicschemical thermodynamics A mechanical foundation of thermodynamics.mechanicalthermodynamics
32 Helmholtz Today 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 … 37 Credit:
Helmholtz’s Results Note from Middle CFrequency C264 D297 E330 F352 G396 A440 B496 38
39 We can study these tones with electronics Tone Or:
Oscilloscope 40
One More Tool 41 Tone Signal Generator Electrical
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 L initial L stretchl L final F
The Guitar Strings 44
Consider Two Situations 45 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.
So… 46 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!
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 … 50 More about this when we do the string thing.
Octave 51