psc-1121 lecture set #1 this week we will have a “pre-test”. we will begin to study time and...

PSC-1121Lecture Set #1

This week

• We will have a “pre-test”.

• We will begin to study time and standards.

• We will begin to use the clickers even though registration lists may not be ready.

• As I write this, I am not sure that WebAssign rosters have been done yet.

Music … What is it?Buddy you're a boy make a big noisePlayin' in the street gonna be a big man some dayYou got mud on your faceYou big disgraceKickin' your can all over the placeSing it!We will we will rock youWe will we will rock youBuddy you're a young man hard manShoutin' in the street gonna take on the world some dayYou got blood on your faceYou big disgraceWavin' your banner all over the placeBuddy you're an old man poor manPleadin' with your eyes gonna make you some peace some dayYou got mud on your faceBig disgrace-Somebody better put you back into your place

But .. What is SOUND???

What Was in the Music

• Rhythm– Timing – what is time? How do you measure it?

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

• Chords– Multiple 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 Clicker Question

A. Yes

B. No

C. 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?

Where did the Queen music come from?

?

? ??

?

Another Issue

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

Observation

• First the lightening

• Then the thunder

• Light travels faster than sound??

• What does this mean??

• Observable: Distance and time

Sound --- A “disturbance”Music is SOUND

How do we explain all of this?

• We use the “scientific method”– Define the fundamentals– Observe under MANY circumstances– Model– Predict– Verify

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

• Gravity

• Quantum Mechanics

• Relativity

• Evolution

BASICS OF SCIENCE

• Careful Measurement based upon standards.

• Theory based upon these measurements

• Predictions based upon the theory

• Verifications of the predictions– Refine the theory– Scrap the theory

Measurements on Objects

• Distance• Time• Amount of material in an object

– Weight??– Mass??

• What about– Color– Shape– Location

Let’s Talk About Time

• Music– The “Beat”– The time between the notes– Indirectly – the tone of the individual notes

• Physics– Objects 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 … ie 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”

Things that “tick” at some rate

• The planet … once a day

• The 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.

Escapement

Spring Wound

Pendulum

Sun Clock

Water Clocks

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.

• Physicist

• Mathematician

• Musician

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

Died: 8 Sept 1894 in Berlin, Germany

A Little Bit about Helmholtz

• Born 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).

1500 1600 1700 1800 1900 2000

GalelioNewton

HelmholtzEinstein

WashingtonMonroe

HaysBeethoven

BrahmsTchaikovsky

Al JolsonBing CrosbyElvis Presley

BeatlesQueen

Historical Perspective

Before moving on …

Let’s quickly review GRAPHS

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.

An Important Graph

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

time

1 box = 1 month

DJI

A (

$)

Another Important Graph

10 years of data – a different view!

6 mos

Back to Helmholtz

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

who the heck is who the heck is millimilli ?? ??

• Milli = 1/1000• Millimeter = 1/1000 meter = 0.001 meter• Milli-second = 1/1000 sec = 0.001 seconds

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

Aside – Helmholtz knew how to do this

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

Resonance (later)

Rotational Speed

(Turns/second)

Loud

ness

Helmholtz Resonators

Resonators

• Each resonator has a certain volume and resonates to a certain tone.

• It resonates to only ONE tome.

• Each one was “tuned” to a different note on the 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 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.

• The outer ring of holes has 12 holes. So one turn produces 12 x R/r puffs.

No .. You don’t have to know this stuff but we can still talk about it.

R

• With a clock, we can measure the time for a turn of the big wheel.

• 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!

Helmholtz’s ResultsNote 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 secondsFrequency=1/6 per sec (Hz) =0.16 sec = 160 ms

Tf

frequency

1

period

1

DISTANCE

• Length 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

The Standard Meter

The Standard Meter

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 Measurement

Measurements

• 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 Measurement

Measurements

• 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 System

Measurements

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

• The 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.

The Metric System

Measurements

Next Tim

e

Next Up – Some Tools

• Scientific Notation• Graphs• Conversion of units

(inches to feet, years to hours)

miles 100.6 6

1 hour = 60 seconds

fini