lecture 1 introduction organization syllabus what is sound? instructor: david kirkby...

Lecture 1IntroductionOrganizationSyllabusWhat is Sound?

Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 1, D. Kirkby 2

IntroductionIn this class, you will learn:

•Something about music•Something about physics•How a physicist thinks

This course is primarily intended for non-science majors.

There is no prerequisite background in physics, mathematics, or music for enjoying and doing well in this class.

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You will be expected to use some basic math skills and be familiar with simple graphs and metric units. Homework assignments will often require numerical answers.

Refer to Sections A.1-A.4 in the Appendix of your textbook to get an idea of the level of math I am expecting (but don’t worry about logarithms).

You should not need any skills beyond what is required to fill out your taxes or understand the kinds of graphs you might find in a newspaper.

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What is Music?We will spend the next 10 weeks answering this question from a physicists perspective…

E = ma2

E = mb2

E = mc2

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Acoustics: The Science of SoundPhysics does not tell us which sounds are “musical” and which are just “noise”.

So this course is really about sound rather than music. But we will focus our study on examples relevant for music. For example, how does a trombone work?

In addition to physics, we will touch on some chemistry and biology.

This course could also be called “The Science of Sound” which is also known as Acoustics.

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What is Physics?Physics aims to describe the physical world.

One of the central ideas of physics is reductionism.

A physicist analyzes a physical process by reducing it to a few key features.

Studying these key features can reveal patterns that are common with other (seemingly unrelated) physical processes.

Patterns are generalized into physical theories.

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Example 1 : A Physicist’s PerspectiveWhat are the key features ofthis scene if we are interested inunderstanding the force ofgravity?

Gravity

Tensionθ

v

The child is a mass acted uponby gravity and by the tensionof the swing.

The child’s position can bedescribed by an angle and avelocity.

Etc…

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Example 2 : A Physicist’s PerspectiveWhat are the key featuresof this scene forunderstanding gravity?

The earth and moon aretwo massive bodies actedupon by their mutualgravity and the sun’sgravity.

Etc…

Gravity

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These 2 examples of very different phenomena have key features in common if we are interested in studying gravity.

For example, the attraction between two massive objects decreases with the square of their separation distance.

A physicist generalizes patterns like this to develop and then test a fundamental physical theory.

The real power of a fundamental physical theory is its generality.

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Organization of this CourseRefer to your handout and the following pages on the course web site :

•Home page•Organization•Syllabus•Calendar

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What is Sound?

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A Physicist’s Reduction of SoundSound has an infinite variety of forms…

Thinking as physicists, what key features can we identifythat are common to all forms of sound?

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Key Features of SoundAll sound has…

…a source…

…which may or notbe detected.

Sound travels through air from source to detector.

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Organizing PrincipleThis reduction will serve as the organizing principle for this course:

Sound = Source + Propagation ( + Detection)

We will study different sources later in this course:•Musical instruments•Human voice•Loudspeakers

We will also study various detectors:•Human ears•Microphones

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Before turning to the production and detection of sound, we will study how sound travels the distance between its source and where it is detected.

This process captures the essence of sound: however a sound is produced or detected, it must travel through some medium (usually air).

Therefore, we can learn everything there is to know about a sound by studying how it travels through air.

(This is amazing considering the variety of possible sounds!)

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From Source to DetectorAlthough we will spend most of this course on sources and detectors, we start today by considering how sound travels between a source and its detector.

Sound travels through a medium which is usually air but could also be a liquid or even a solid (eg, your jaw bone).

Air consists of many particles behaving almost independently, exceptwhen they hit eachother. Most of theparticles in air arenitrogen molecules.

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More About AirAn “empty” bottle contains about 1022 particles!

The particles in a bottle are constantly moving and bumping into each other and the walls of the bottle.

The temperature of the air measures the average energy of all this motion.

The density of the air measures the mass of all the particles in a unit volume. The ~1022 particles in an “empty” bottle have a mass of about 1 gram.

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A particle bumping into the wall of a bottle gives it a tiny jolt. Because there are so many particles (~1022) in the bottle, these jolts add up to a huge force equivalent to about a 1 tonne (1000kg) weight!

Why doesn’t the bottle explode??

The pressure of the air measures the forces due to all of the collisions of its molecules, and is usually measured in kilopascals (1 kPa = 0.145 psi).

Normal air pressure is about 100 kPa.

Blaise Pascal, 1623-62

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Air pressure decreases with altitude by about 1% / 100m.

Air pressure varies with weather patterns. The differences between high and low pressure regions are typically 2-3% of the global average pressure.

Wind tends to flowfrom high to lowpressure regions.

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Air pressure is greater inside a tire, basketball or balloon.

A bicycle tire inflated to 50 psi contains air at a pressure of about 3x the pressure of the atmosphere.

The extra force of all this pressure inside the tire is balanced by the elasticity of the rubber.

What balances the force of collisions for the air in this room? Why doesn’t the atmosphere spread out into space like a punctured tire?

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Online DemonstrationVisit this page to see simulations of air particles and the effects of changing temperature and density.

Pressure depends on density and temperature.

How do you expect the air pressure to change if:•The air temperature increases?•The air density increases?

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Back to SoundSound is a periodic (repetitive) disturbance of a medium (usually air).

What are the properties of a periodic disturbance?•Repetition rate•Speed of disturbance•Size of disturbance•Repetition distance

Visit this page to see simulations of air particles disturbed by sound and learn about these properties.

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Repetition RateThe number of times the disturbance repeats per second is called its frequency and is usually measured in Hertz(1 Hz = 1 cycle/sec).

For sound, frequency relates to how high (treble) or low (bass) a sound appears.

What range of frequencies can youactually hear?

The reciprocal of frequency is the timeit takes for a disturbance to repeat. We callthis the period. Heinrich Hertz, 1857-94

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The Speed of SoundThe speed at which a disturbance propagates through a medium is an intrinsic property of the medium and (to a good approximation for air) does not depend on the type of disturbance.

We call this the speed of sound and measure it in m/s.Its value is about 340 m/s for the air in this room, and it varies slightly with temperature and pressure.

The speed of sound in water is much faster (about 1500 m/s) than in air at the same temperature. Why?

Sound does not travel at all in space! Why?

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Size of DisturbanceNormal levels of sound correspond to tiny disturbances compared with the huge forces (~ 1 tonne on a bottle) of normal atmostpheric pressure.

The disturbances created by my speech now are only adding (or subtracting) a force equivalent to about 1 gram on a bottle, or only about one millionth of the base atmospheric pressure.

Larger disturbances correspond to louder sounds.

We call the size of a disturbance its amplitude. The typical back and forth motion of air particles due to normal sound levels is only about 1 millionth of a meter.

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Repetition DistanceThe distance between peaks of a disturbance is called the wavelength and is usually measured in meters.

The typical wavelengths for my speech in this room are about 1 meter.

The wavelength, frequency (or period) and speed of sound are related by the following equation:

speed = wavelength = wavelength x frequency period

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Sources and Detectors of SoundThe demonstrations modeled sources and detectors of sound as generic solids that vibrate in synch with the air around them.

This is exactly the kind of the general pattern a physicist looks for!

The key to our study of detectors and sources of sound will be to:

•identify their moving parts that respond to or drive repetitive disturbances in the air around them, and

•understand the motion of these moving parts.

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SummarySound = source + transport ( + detector)

Sound is transported through a medium (usually air) as a periodic disturbance of its molecules.

We compared sound with other types of air disturbance due to changing elevation or weather, or pumping up a tire.

v = λ fspeed

wavelength

frequency

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Review QuestionsThe collisions of air particles against the inside of a bottle exert a force equivalent to a 1 tonne weight. Why doesn’t the bottle explode?

The air around you is under a lot of pressure. What is holding it in?

How does air pressure depend on temperature and density?

Do particles of air have to travel from a person’s mouth to you ear in order for you to hear them?

Why can’t you hear an explosion in space?

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Survey: What is Your Background?Part of your first homework assignment is to complete an online survey that will give me a picture of your background in:

•Mathematics•Physics•Music

There are no wrong answers, but you will get credit for completing this survey.

Giving accurate answers will help me make the course more suitable for you.