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Gunther L. The Physics of Music and Color

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Gunther L. The Physics of Music and Color
Springer, 2012. — 548 p.
This textbook has its roots in a course that was first given by Gary Goldstein and me at Tufts University in 1971. Both of us are theoretical physicists, with Gary focusing on the study of elementary particles and me focusing on condensed matter physics, which is the study of the fundamental behavior of various types of matter – superconductors, magnets, fluids, among many others. However, in addition, we both have a great love and appreciation for the arts. This love is fortunately also manifested in our involvement therein: Gary has been seriously devoted to oil painting. I have played the violin since I was seven and played in many community orchestras. I am also the founder and director of a chorus. Finally, I am fortunate to have a brother, Perry Gunther, who is a sculptor and my inspiration and mentor in the fine arts.
It is common to have a course on either the Physics of Music or the Physics of Color. Numerous textbooks exist, many of which are outstanding. Why did we choose to develop a course on both music and color? There are a number of reasons:
1. The basic underlying physical principles of the two subjects overlap greatly because both music and color are manifestations of wave phenomena. In particular, commonalities exist with respect to the production, transmission, and detection of sound and light. Our decision to include both music and color was partly due to the fact that some wave phenomena are relatively easy to demonstrate for sound but not for light; they are experienced in everyday life. Examples include diffraction and the Doppler effect. Thus, the study of sound helps us understand light. On the other hand, there are some wave phenomena – common to both sound and light – that are more easily observed for light. An example is refraction, wherein a beam of light is traveling through air and is incident upon a surface of glass. Refraction causes the beam to bend upon passing into the glass. Refraction is the basis for the operation of eyeglasses. And finally, there are wave phenomena that are easily observable for both sound and light. Interference is an example.
Two stereo loudspeakers emitting a sound at the same single frequency produce dead (silent) regions within a room as a result of the interference between the two sound waves produced by the two loudspeakers; the colors observed on the CDs of the photo in the frontispiece are a result of the interference of light reflected from the grooves within the CDs.
2. The production of music and color involves physical systems, whose behavior depends upon a common set of physical principles. They include vibrating mechanical systems (such as the strings of the violin or the drum, vibrating columns of air in wind instruments and the organ), electromagnetic waves such as light, the rods and cones of the eye, and the atom. All manifest the existence of modes and the phenomena of excitation, resonance, energy storage and transfer, and attenuation.
CDs produce sound through a series of processes that involve many distinct physical phenomena. First, the CD modulates a laser beam that excites an electronic device into producing an electrical signal. The laser light itself is a manifestation of electric and magnetic fields. The electrical signal is used to cause the cone of a loudspeaker to vibrate and produce the motion in air that is none other than the sound wave that we hear.
3. The course that led to the writing of this book offers us the opportunity to study a major fraction of the basic principles of physics, with an added important feature: Traditionally, introductory physics courses are organized so that basic principles are introduced first and are then applied wherever possible. This course, on the other hand, is based on a motivational approach: Because of the ease of observing most phenomena that is afforded by including both light and sound, we are able to introduce the vast majority of topics using class demonstrations.
We challenge ourselves by calling for a physical basis for what we observe. We turn to basic principles as a means of understanding the phenomena. A study of both subjects involves pretty nearly the entire gamut of the fundamental laws of classical as well as modern physics. (The main excluded areas are nuclear and particle physics and relativity.)
Ultimately, our approach helps us appreciate a central cornerstone of physics – to uncover a minimal set of concepts and laws that is adequate to describe and account for all physical observations. Simplification is the motto. We learn to appreciate how it is that because the laws of physics weave an intricate, vast web among physical phenomena, physics (and science generally) has attained its stature of reflecting what some people refer to as truth and, much more significant, of having an extraordinarily high level of dependability.
Introductory Remarks
The Vibrating String
The Vibrating Air Column
Electricity, Magnetism, and Electromagnetic Waves
The Atom as a Source of Light
The Principle of Superposition
Propagation Phenomena
The Ear
Tuning, Intonation, and Temperament: Choosing Frequencies for Musical Notes
The Eye
Characterizing Light Sources Color Filters and Pigments
Theory of Color Vision
A: Symbols
B Powers of Ten: Prefixes
C: Conversion of Units and Special Constants
D: References for the Physics of Music and Color
E: A Crude Derivation of the Frequency of a Simple Harmonic Oscillator
F: Numerical Integration of Newton’s Equation for a SHO
G: Magnifying Power of an Optical System
H: Threshold of Hearing, Threshold of Aural Pain, and General Threshold of Physical Pain
I: Transformation Between Tables of Color-Matching Functions for Two Sets of Monochromatic Primaries
J: Hommage to Pierre-Gilles de Gennes: Art and Science
K: MAPPINGS as a Basis for Arriving at a Mutually Agreed Upon Description of Our Observations of the World – Establishing ‘Truths’ and ‘Facts
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