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

Hojadu?

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

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!

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!

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

Graph Stationary Friction Newtons Moving Force Newtons

Applied force W f N

Frictional Force Stationary Sliding Applied Force

Friction

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

The Violin – Friction in Motion!

The Bow Horsehair

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

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

Application ?? Physics Later

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

The Spring

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

Springs Oscillate

Graph

Important Result for a Spring:

So ….

A string is just a spring misspelled!

Concept … Tension

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!

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

The Guitar Strings

Stringed Instruments PLUCK Momentum

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

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

Remember Helmholtz 1821 - 1894 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.

Helmholtz  Today The SINE curve

Two Fuzzy Sine Waves

We Know (And will know even more later) Tone

Today’s Approach

Speaker

Into the air … Credit: http://www.soundonmind.com/

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

We can study these tones with electronics Or:

Oscilloscope http://commons.wikimedia.org/wiki/Main_Page

One More Tool Tone Signal Generator Electrical

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.

The Spring

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

Springs Oscillate

Graph

Important Result for a Spring:

So ….

A string is just a spring misspelled!

Concept … Tension

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!

Another piece of the string! Lstretchl Linitial F Lfinal

The Guitar Strings

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.

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!

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).

Now …. lets look at the MONOCHORD

HAVE FUN!

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

Octave