PSC-1121 Lecture Set #1 Introductory Concepts

This week We 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: ucf Password: ihatephysics (change to something else)

But.. What kind of SOUND??? What is Music?

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 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? This would have been a clicker question.

Where did the music come from?

Another Issue

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 What the

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. 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) Gravity Quantum Mechanics Relativity Evolution String Theory (The only one that is shaky).

BASICS OF SCIENCE Careful Measurement based upon standards. Theory based upon these measurements Predictions based upon the theory Verifications of the predictions Leave the theory as is Refine the theory Scrap the theory

The Mind Fart

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 (later) The time the music takes in getting to the ear of the listener. The time it takes to download it?? 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 … 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 seconds” The process took 3.76 fempto seconds.

Sun Clock

Water Clocks

Things that “tick” at some rate The planet … once a day The Pendulum.. Depends on a number of things; Parameters: Length Weight, whatever that is. Mounting

In case you care….. We will discuss this “g-thing” when we get 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 Or:

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 of Pendulum

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).

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 DJIA ($)

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 open closed

1 milli-second 1/1000 second second seconds (later, but see the same document).

The Graph open closed puff

10 puffs in 10 milli-seconds

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) Loudness

Helmholtz Resonators

Aside – Helmholtz knew how to do this

Resonators Each 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 Again This is faster than Helmholtz could see. How did he measure it?? 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 2  R. The second, smaller (inner) wheel turns the same “distance”. That distance results in many more turns. The number of turns is 2  R/ 2  r=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 CFrequency C264 D297 E330 F352 G396 A440 B496

Today, we use a “scope” Oscilloscope

A Bit Magnified (poor resolution)

Another Graph.. “sine curve” Time (seconds) disturbance

Time (seconds) disturbance 6 sec Period = 6 seconds 1 oscillation=6 seconds f=1oscillation/6 seconds Frequency=1/6 per sec (Hz) =0.16 sec = 160 ms

0.16 sec = 160 ms

Let’s look at DISTANCE

How Big?

DISTANCE Length or Distance How “far” something moves or travels. Measured against some agreed upon standard. Length Standard.. The Gorf Unknown Length /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 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.

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

Yard The 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, mile Weight: pound, ton, ounce Time: seconds A very small length might be inch. Not convenient.