Physics 1200: Behind the Music

Aka “Musical Acoustics” or “Science of Sound”

Cluster: “The Science Behind the Music” [ Psych 1002, Physics 1200, Music 1085 ]

“Dr. Bill” PezzagliaPhysics Dept

CSU East Bay

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Notes • Lecture Notes can be downloaded at:

http://www.clifford.org/drbill/csueb/

• TextBook:– Donald E. Hall, Musical Acoustics

(3rd edition) [Brooks/Cole 2002]

• References (more advanced)

– Rossing, Moore & Wheeler, “The Science of Sound”(3rd ed, Addison Wesley 2002)

– Fletcher & Rossing, “The Physics of Musical instruments”(2nd ed, Springer 1998)

– Olson, “Music, Physics & Engineering” (2nd ed, Dover 1967)

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Physics 1200 (Musical Acoustics)

Topic 01

Introduction to Acoustics

Updated 2015Jan05

Dr. Bill Pezzaglia

Physics CSUEB

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Outline

I. Intro to Acoustics

A. What is “Acoustics”

B. Nature of Sound Waves

C. Speed of Sound

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A. What is “Acoustics

1. Root of the Word

2. Classes of Sound

3. What we study in this class

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1. The term: “Acoustics”

a) Joseph Sauveur (1653-1716) coined the term acoustique, which he derived from the ancient Greek word ακουστός, meaning "able to be heard".

b) Acoustics is the interdisciplinary science that deals with the study of sound (all mechanical waves in gases, liquids, and solids)

c) Musical acoustics or music acoustics is the branch of acoustics concerned with researching and describing the physics of music .

Reference: wikipedia

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2. Classes of Sound

a) Ultrasound: above hearing(sonograms!)

b) Infrasound: below hearing(earthquakes!)

c) Audible Sound(between 20 and 20,000 oscillations per second)

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3. What we study

a) Production of sound(instruments, speakers)

b) Propagation of sound(waves)

c) Perception of sound(Psychoacoustics: ear, harmony)

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B. The Nature of Sound

1. Wave Modes

2. Structure of a wave

3. Sound waves

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1. Types of Waves (a) Longitudinal (“p” waves) travel through gas, liquid and

solids. Particle motion in direction of wave

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(b) Transverse (“s” waves) travel only in solids. Particle motion perpendicular to direction of wave.

(c) Surface Waves • Ocean Waves are “Cycloid” Waves. Particles travel in

circles.

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• Rayleigh Waves (“R” wave) are similar, but exist in solids (more damaging in earthquakes than “p” or “s” waves)

(c) Light Waves • Light is a wave of electric and magnetic phenomena that can travel

through empty space (no medium!)

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(d) Gravity Waves? • Not discovered yet, but we are looking for them.

They would distort space as they travel by!

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2. The Structure of a Wave

a) Nodes: no displacement

b) Antinode: maximum displacement

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Wave parameters

(c) Wavelength (measured in meters)

(d) Amplitude (loudness) is the maximum wave displacement

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3. What is the “wave” of sound? (a) Aristotle: suggested that the movement of air

carries sound to our ears, and if there is no air, there will be no sound.

• Sound is immaterial. For it is not air, but it is the form about the air and the appearance after some sort of percussion which becomes sound; and every appearance is immaterial; for it moves with bodies, but is itself absolutely immaterial; as in the case of a bent rod the surface-appearance suffers no change, but the matter is what is bent.

• …air motion is generated by a source, "thrusting forward in like manner the adjoining air, to that the sound travels unaltered in quality as far as the disturbance of the air manages to reach."

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Aristotle 384 BC-322 BC

3b. Marcus Vitruvius Pollio

• Roman Engineer (ca. 80/70 BC- ca. 25 BC)

• Realizing that a vibrating string strikes the air many times in a series of blows, not just once

• suggests that the air not only moved, but vibrated in response to the vibrations of the string.

• Proposes that what we hear as sound are these air vibrations.

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3c. Sound is displacement of pressure 18

• Rarefaction: the “trough” of the wave where pressure (density) is low• Compression: the “peak” of the wave where pressure (density) is high

C. The Speed of Sound

1. Wave Speed vs Particle Speed

2. Speed and Density of Medium

3. Dispersion

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1. Wave speed vs Displacement Speed a) Wavespeed: is how fast the nodes (or antinodes) are moving. In air, all

sounds move the same speed whether loud, soft, high or low.b) Particle (Displacement) Speed: is how fast the particles in the medium are

moving, which can be quite different! This is related to the intensity of the sound (soft sound they move slowly and not very far)

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c) In a “standing wave”, the particles are moving but the wave is not moving at all!

2a. Speed of sound is finite

• Leonardo da Vinci(1452-1519)

• A bell far away, will be heard to resonate in response to a bell ringing, after a delay in time.

• 1500 Did he measure the speed of sound? (some references say yes).

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2b Speed of sound depends upon medium!

• (1640) classic experiment on the sound radiation by a ticking watch in a partially evacuated glass vessel provided evidence that air is necessary, either for the production or transmission of sound.

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Robert Boyle (1627-1691 AD)

2c Measurement of Speed of Sound

• William Derham (1657-1735)First to accurately measure speed of sound (in air)(341 meters/second)

• Newton used his value in the Principia (1686), although it was 16% higher than the value Newton theoretically calculated.

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2d Speed of Sound in Water (1826)

Ion Lake Geneva, Switzerland, Jean-Daniel Colladen, a physicist, and Charles-Francois Sturm, a mathematician, measured speed to be 5x faster than in air.

In their experiment, the underwater bell was struck simultaneously with ignition of gunpowder on the first boat. The sound of the bell and flash from the gunpowder were observed 10 miles away on the second boat. The time between the gunpowder flash and the sound reaching the second boat was used to calculate the speed of sound in water.

Speed did NOT depend upon frequency!

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2e Ernst Chladni (1756—1827)

• First measurement of speed of sound in solids (up to 40x faster than in air!)

• Measures speed of sound in different gases(slower in heavier gases)

• 1787 “Chladni Plate” shows vibration of sound using sand on a plate.

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3. Dispersion

(a) Sound in air is “non-dispersive”, meaning speed is independent of the frequency of the sound

• Gassendi demonstrated speed of sound is independent of pitch by comparing measurements from cannon and rifle (no “dispersion”)

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Pierre Gassendi (1592-1655)

3b Dispersive Media

• Sound in some media (e.g. metal plates) is very dispersive.

• Speed of sound usually increases with frequency (in metal)

• This creates “inharmonics” in instruments (bells, xylophones, strings)

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References & Notes

• Ruben’s Tube Demo:– http://www.youtube.com/watch?v=kQ6jYR0-svE– http://www.youtube.com/watch?v=JD90K6KfQes– http://www.youtube.com/watch?v=EhnbhOoPIBc– Mythbusters: http://www.youtube.com/watch?v=ynqzeIYA7Iw

• Dispersion of sound waves– Part 1: http://www.youtube.com/watch?v=HtUGYKjG09g– Part 2: http://www.youtube.com/watch?v=rm8cMV95gWY

• Echo Tube (shows dispersion of sound)– http://www.youtube.com/v/H9LocUJCR5c– http://www.youtube.com/watch?v=H9LocUJCR5c– http://www.youtube.com/watch?v=IYRoWutoyxM

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Things to do

• x

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