PSC-1121Lecture Set #1

Introductory Concepts

This weekWe will have a “pre-test”.We will begin to study time and standards

and periodic variations.We will begin to use the clickers on

Monday.Be sure to register for WebAssign

Username: PID without leading letter or leading zero

Institution: ucfPassword: ihatephysics (change to something

else)

But .. What kind of SOUND???

What is Music?

What Was in the MusicRhythm

Timing – what is time? How do you measure it?Notes

Musical tones – What are they? How do you know?

ChordsMultiple tones sounded together – WHY do they

sound good TOGETHER?Voice

How does that work? Why does it sound good?Words … meaning. But words are not necessary!

Unfair Question

A. YesB. NoC. Too early in the morning

to think about this kind of stuff!

If a tree falls in a forest and there is nobody around to hear it fall, does it make a sound?

This would have been a clicker question.

Where did the music come from?

Another Issue

http://www.youtube.com/watch?v=F0WykZvfg_k&NR=1

ObservationFirst the lighteningThen the thunder

Light travels faster than sound??What does this mean??

Observable: Distance and time

Sound --- A “disturbance”Music is SOUND

What the

*&^@?

How do we explain all of this?We use the “scientific method”

Define the fundamentalsObserve under MANY circumstancesModelPredictVerify

If this doesn’t work, scrap or modify the theory.

The theory must explain everything it is supposed to explain or it is dog poo.

Keep the loop going … forever!

Examples of Scientific “Theories”

Newtonian Mechanics (in its realm of applicability)

GravityQuantum MechanicsRelativityEvolutionString Theory (The only one that is shaky).

BASICS OF SCIENCECareful Measurement based upon

standards.Theory based upon these measurementsPredictions based upon the theoryVerifications of the predictions

Leave the theory as isRefine the theoryScrap the theory

The Mind Fart

Measurements on ObjectsDistanceTimeAmount of material in an object

Weight??Mass??

What aboutColorShapeLocation

Let’s Talk About TimeMusic

The “Beat”The time between the notesIndirectly – the tone of the individual notes

(later)The time the music takes in getting to the ear

of the listener.The time it takes to download it??

PhysicsObjects move in time so time is an important

variable in describing motion.We will do a lot of this.

Approaches to TIME TIME

The subjective “distance” between two EVENTS.It needs to be objective … i.e. measurable

and reproducible. Original Clock – The Earth’s Rotation

“It is two days journey”Today’s Clocks –

“He ran the race in 4 hours, 2 minutes and 21.85 seconds”

The process took 3.76 fempto seconds.

Sun Clock

Water Clocks

Things that “tick” at some rate

The planet … once a dayThe Pendulum .. Depends on a number of

things;Parameters:

Length

Weight,whateverthat is.

Mounting

In case you care…..

2/32

1415926.3

(g)

(L) 2

sftg

gravityofonaccelerati

Lengthperiod

We will discuss this “g-thing” when weget to acceleration.

PERIOD??If something does something in a repetitive

fashion, then the PERIOD is the time that it takes to go through one single cycle of the motion.

For the pendulum: The time that it takes to go from 1-2-3-2-1.Or: 2-3-2-1-2

Escapement

Spring Wound

Pendulum

And so on …

Rolex (~$10K) Atomic Clock (NASA) $ megabucks

~$200

The music clock: the Metronome

112 quarter notes per minute.

Kind ofPendulum

Now that we can measure TIME, let’s talk about Helmholtz.

PhysicistMathematicianMusician

Hermann Ludwig Ferdinand von Helmholtz Born: 31 Aug 1821 in Potsdam, Prussia, Germany

Died: 8 Sept 1894 in Berlin, Germany

A Little Bit about HelmholtzBorn in 1821; learned the classical

languages as well as French English and Italian. His native language was German.

Initially got a medial degree. While in medical school, he attended physics classes and learned advanced mathematics on his own.

He also learned to play the piano.A classic underachiever!!

More about Helmholtz

He invented the ophthalmoscope and the opthalmometer that allowed for the proper prescription of eyeglasses.

He published “The Handbook of Physiological Optics” (2 volumes).

He wrote “On the Sensation of Tone as a Physiological Basis for the Theory of Music” (1863).

Let’s review graphs.

A Graph is a way of visually presenting data from a table.

It usually has two axes. These axes can be anything but in science it is often an x- and y- axis.

Sometimes a graph is three dimensional.

SEE THE BACKGROUND MATERIAL ON THE WEBSITE

An Important Graph

The Dow Jones Industrial Average (CNN-money 7-08

time

1 box = 1 month

DJI

A (

$)

Another Important Graph:The Good Old Days !!!

10 years of data – a different view!

6 mos

OK … Back to Helmholtz

The Siren … a scientific instrument

The Graph

-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

open

closed

-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

1 milli-second

1/1000 second0.001 second10-3 seconds (later, but see the same document).

The Graph

-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

open

closed

puff

-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

10 puffs in 10 milli-seconds

1-sec 1000 secondper 1000

second"per "0.001

1 /second

0.001 x 10

puffs 10

sec 0.001 x puffs/10 10

dsmillisecon puffs/10 10

The number of times that something (repetitive) happens

in a second is called the

FREQUENCY: f

f=1000 sec-1= 1000 Hertz

New Unit

The Siren Creates A Musical Tone

100 Bottles of beer on the wall (Beer bottles make a sound too!)

Resonance (later)

Rotational Speed

(Turns/second)

Loud

ness

Helmholtz Resonators

Aside – Helmholtz knew how to do this

ResonatorsEach resonator has a certain volume and

resonates to a certain tone.It resonates to only ONE tone.Each resonator was “tuned” to a different

note on the piano. (How did they tune a piano??)

The speed of the siren was adjusted to match the same tone.

The Graph AgainThis is faster than Helmholtz could see.How did he measure it??

-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

open

closed

Back to the Siren

12 holes in the outer ring

Back in his laboratory

R

For each turn of the large wheel, the smaller wheel will turn MORE.

We can figure out this “leverage” from the two radii.

We won’t dwell on the calculation. For those who are interested, though ….

R

R

Turn the big wheel once. The belt will travel a distance 2R.

The second, smaller (inner) wheel turns the same “distance”. That distance results in many more turns.

The number of turns is 2R/ 2r=R/r.Assume outer ring of holes has 12 holes. So

one turn produces 12 x R/r puffs.

R

With a clock, we can measure the time for a turn of the big wheel. (Or a pendulum whose frequency can be calculated).

The number of puffs .. That is the frequency per timed turn is now known.

You can now demonstrate the correspondence between particular “note” on the piano with a frequency!

Dr. Helmholtz’s Results

Note from Middle C Frequency

C 264

D 297

E 330

F 352

G 396

A 440

B 496

Today, we use a “scope”Oscilloscope

A Bit Magnified (poor resolution)

Another Graph .. “sine curve”

-1.5

-1

-0.5

0

0.5

1

1.5

0 5 10 15 20 25

Time (seconds)

dis

turb

an

ce

-1.5

-1

-0.5

0

0.5

1

1.5

0 5 10 15 20 25

Time (seconds)

dis

turb

an

ce

6 sec

Period = 6 seconds1 oscillation=6 secondsf=1oscillation/6 secondsFrequency=1/6 per sec (Hz) =0.16 sec = 160 ms

Tf

frequency

1

period

1

0.16 sec = 160 ms

ms 160 ms 1000 x 16.0sec

ms 1000 sec 0.16

Let’s look at DISTANCE

How Big?

How Big?

DISTANCELength or Distance

How “far” something moves or travels.Measured against some agreed upon standard.

Length Standard .. The Gorf

Unknown Length

1 2 3 4 1/8

= 4 1/8 Gorfs

Measurements

If someone offered to sell a bar of gold for $200, you would immediately ask, “How large is the bar?” The size of the bar obviously determines

whether it is a good buy. A similar problem existed in the early days

of commerce. Even when there were standard units of

measure, they were not the same from time to time and region to region.

Later, several standardized systems of measurement were developed.

Systems of MeasurementMeasurements

The two dominant systems are the U.S. customary system, based on the foot, pound, and second, and the metric system, based on the meter, kilogram, and second.

Thomas Jefferson advocated that the United States adopt the metric system, but his advice was not taken. As a result, most people in the United States do not use the metric system. It is used, however, by the scientific community and those who work on such things as cars. England and Canada have now officially changed

to the metric system. The United States is the only major country not to have made the change.

Systems of MeasurementMeasurements

There are obvious advantages in having the entire world use a single system.

The metric system has advantages over the U.S. customary system and was the system chosen in 1960 by the General Conference on Weights and Measures. The official version is known as Le Système International d’Unités and is abbreviated SI.

The Metric SystemMeasurements

Smaller distances are measured in such units as the centimeter (cm). centi = one-hundredth; 100 centimeters = 1

meterThe other prefixes are given on the next slide

(Table 1-3 in text) along with their abbreviations and various forms of their numerical values.

This stuff is a real pain. Most if the music related stuff in this course will be done in the so-called English System – feet, pounds,seconds.

Let’s Look at Length

The Foot - Length

The average foot length is about 9.4 inches (240 mm) for current Europeans. Approximately 99.6% of British men have a foot that is less than 12 inches long. One attempt to "explain" the "missing" inches is that the measure did not refer to a naked foot, but to the length of footwear, which could theoretically add an inch or two to the naked foot's length

YardThe length from some English Kings nose to

the tip of his outstretched hand.This was an inconvenient standard.Probably not true for very long.

Today, the FOOT is 1/3 of a yard.

To build a road 2 miles long, do we need a one mile standard? Not.

In the “English System”, we use the following:Length: inch, foot, yard, mileWeight: pound, ton, ounceTime: seconds

A very small length might be 0.000023 inch.Not convenient.

1500 1600 1700 1800 1900 2000

GalelioNewton

HelmholtzEinstein

WashingtonMonroe

HaysBeethoven

BrahmsTchaikovsky

Al JolsonBing CrosbyElvis Presley

BeatlesQueen

Historical Perspective