psc-1121 lecture set #1 this week we will have a “pre-test”. we will begin to study time and...
TRANSCRIPT
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PSC-1121Lecture Set #1
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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.
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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
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But .. What is SOUND???
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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!
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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?
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Where did the Queen music come from?
?
? ??
?
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Another Issue
http://www.youtube.com/watch?v=F0WykZvfg_k&NR=1
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Observation
• First the lightening
• Then the thunder
• Light travels faster than sound??
• What does this mean??
• Observable: Distance and time
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Sound --- A “disturbance”Music is SOUND
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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!
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Examples of Scientific “Theories”
• Newtonian Mechanics (in its realm of applicability)
• Gravity
• Quantum Mechanics
• Relativity
• Evolution
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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
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Measurements on Objects
• Distance• Time• Amount of material in an object
– Weight??– Mass??
• What about– Color– Shape– Location
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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.
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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”
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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
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In case you care…..
2/32
1415926.3
(g)
(L) 2
sftg
gravityofonaccelerati
Lengthperiod
We will discuss this “g-thing” when weget to acceleration.
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Escapement
Spring Wound
Pendulum
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Sun Clock
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Water Clocks
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And so on …
Rolex (~$10K) Atomic Clock (NASA) $ megabucks
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~ $200
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The music clock: the Metronome
112 quarter notes per minute.
Kind ofPendulum
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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
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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!!
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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).
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1500 1600 1700 1800 1900 2000
GalelioNewton
HelmholtzEinstein
WashingtonMonroe
HaysBeethoven
BrahmsTchaikovsky
Al JolsonBing CrosbyElvis Presley
BeatlesQueen
Historical Perspective
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Before moving on …
Let’s quickly review GRAPHS
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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.
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An Important Graph
The Dow Jones Industrial Average (CNN-money 7-08
time
1 box = 1 month
DJI
A (
$)
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Another Important Graph
10 years of data – a different view!
6 mos
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Back to Helmholtz
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Siren … a scientific instrument
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The Graph
-0.2
0
0.2
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1
1.2
0 2 4 6 8 10 12
Time in milli-seconds
"air
spee
d"
- re
lati
ve
open
closed
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Time in milli-seconds
"air
spee
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- re
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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
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The Graph
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1
1.2
0 2 4 6 8 10 12
Time in milli-seconds
"air
spee
d"
- re
lati
ve
open
closed
puff
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-0.2
0
0.2
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0.6
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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
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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
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The number of times that something (repetitive) happens
in a second is called the
FREQUENCY: f
f=1000 sec-1= 1000 Hertz
New Unit
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The Siren Creates A Musical Tone
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Aside – Helmholtz knew how to do this
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100 Bottles of beer on the wall (Beer bottles make a sound too!)
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Resonance (later)
Rotational Speed
(Turns/second)
Loud
ness
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Helmholtz Resonators
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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.
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The Graph AgainThis is faster than Helmholtz could see.
How did he measure it??
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Time in milli-seconds
"air
spee
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open
closed
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Back to the Siren
12 holes in the outer ring
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Back in his laboratory
R
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• 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
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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.
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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!
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Helmholtz’s ResultsNote from Middle C Frequency
C 264
D 297
E 330
F 352
G 396
A 440
B 496
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Today, we use a “scope”Oscilloscope
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A Bit Magnified (poor resolution)
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Another Graph .. “sine curve”
-1.5
-1
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1
1.5
0 5 10 15 20 25
Time (seconds)
dis
turb
an
ce
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-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
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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
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The Standard Meter
The Standard Meter
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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.
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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.
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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.
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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.
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The Metric System
Measurements
Next Tim
e
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Next Up – Some Tools
• Scientific Notation• Graphs• Conversion of units
(inches to feet, years to hours)
miles 100.6 6
1 hour = 60 seconds
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fini