Note:  To run the AVI file simulations, click on the simulation image to start and stop the motion.

Introduction to the Fundamentals of Sound
Key words:  velocity, frequency, and wavelength, transverse and longitudinal waves, power and intensity.

TYPES OF MECHANICAL WAVE MOTION
Transverse waves cause medium displacements perpendicular to the direction of the propagation of the wave.  Example:  Wire vibrating under tension.
Longitudinal waves cause medium displacements in the same direction as the propagation of the wave.  Example:  Vibrating column of air in a tube.

Intensity is the power per unit area of a sound wave emanating from a point source and varies as the inverse square of the distance.

The intensity is a function of the properties of the medium, the frequency of the sound, and the actual amplitudes of the molecular motions.
Speed of propagation is dependent upon the nature of the material.
* Strings (Transverse):  Tension (F), mass per unit length
* Gases (Longitudinal):  Temperature, molecular mass

The home page of the Acoustical Society of America contains much useful information.
Their “About Acoustics” section has an excellent article “ The Wave Theory of Sound ”.
 

Interference of sound waves
Key words:   superposition, beats, coherent sound waves, interference, dispersion, standing waves.

SUPERPOSITION is the addition of two waves of differing phase.
Phase determines whether we have constructive or destructive interference
Beats is the addition waves of slightly differing frequency.

STANDING WAVES result from the addition of oppositely traveling waves.
Antinodes (Maximum amplitude )
Nodes (Minimum amplitude)

You get different interference patterns (i.e., location of the nodes) depending on the separation and wavelengths of the sources.

Observing Sound Phenomena
Key Words:   Doppler effect, sonic “boom”.

The DOPPLER  EFFECT is a change in the frequency (or wavelength) of a wave due to relative motion between the source (S) and observer (L = listener).

Decrease in frequency => source and observer receding.
Increase in frequency => source and observer approaching.

The Astronomical Doppler Shift is important for light.
Red shift =>  source and observer receding.
Blue shift =>  source and observer approaching.

A Sonic “Boom” is an acoustical shock wave. If v is the speed of sound in the medium, and u is the speed of the object, then the mach number is M = u/v.

On 14 October 1997, PBS broadcast a NOVA program on breaking the sound barrier.  Their web site has several interesting and educational items pertaining to supersonic travel including sonic booms.

Two other links on sonic booms of interest are:  Space Shuttles and Sonic Booms (NASA) , and USAF FACT SHEET 96-03.
 

Human Factors and Sound
Key Words:  human voice, human ear, human acoustical factors.

The Decibel scale compares intensities and is a logarithmic scale.
0 dB is the threshold of human hearing.

World Forum for Acoustic Ecology has many useful links.
 

Musical Instruments and Acoustics
Key Words:  harmonic (overtone), vibrating string, vibrating column of air, reflected sound, room acoustics, resonance.

STANDING WAVES IN AIR COLUMNS:  No displacement at closed ends (node).  Maximum displacement at open ends (antinode).

STANDING WAVES ON A STRING:  An integral number of half wavelengths must fit on the string.  Normal modes of oscillation for a string fixed at both ends:

n = 1 First Harmonic Fundamental
n = 2 Second Harmonic First Overtone
n = 3 Third Harmonic Second Overtone
n =... nth Harmonic (n-1)th Overtone

RESONANCES are the normal modes of oscillation in physical systems with a natural or resonant frequency.  When driving frequency f is near fo, amplitude increases.
Examples:
* Sympathetic tuning forks
* Tuner circuit on a radio (E-M resonance)
* Driven vibrating string (lab)
* Tuning fork near air column
* Human voice
* Mechanical systems
* Singing in the shower

Musical acoustics are based on the principles of superposition, normal modes of oscillation, and resonance.
Harmonics:  Instruments sound different because of the mix of harmonics.  Sound is really a complex mixture of many fundamental frequencies and higher harmonics.  Analyzed with the Fourier Series:

Resonance:  Resonance "chambers" amplify the sound and effect the harmonic mix.

Echoes:  Reflected sound is key factor in concert hall design.
* Reverberation time different for different music:  Gabrielli's antiphonal music in San Marco.
* Flairs disperse the sound.
* People absorb sound and an empty hall sounds much different than a full hall.  Possible to "tune" a hall, cf. Ordway Music Theatre (St. Paul) and Ted Mann Hall, University of Minnesota, have moveable panels to change sound reflection.
* Musicians need to hear one another, use reflective shell behind chorus.
Good halls:  Ted Mann, Orchestra Hall, St. Mark's Cathedral.
Bad halls:  State Theatre, many churches (due to carpeting and low ceilings).

Psychoacoustics:  How we perceive sound depends on several factors:
* Key (Major/Minor)
* Dissonance or harmony, rhythm, mixture of overtones.

Musical instruments differ in sound because of the relative intensity of different harmonics.
Most orchestras tune on the oboe because of the relatively pure sound.  Strings go flat with playing, winds go sharp with playing.

Vocal Music:  the difference between a male and a female singing the same note is the mixture of harmonics (i.e., overtones).

Here are some web sites that contain material on musical acoustics:  “Music Physics ” (Pacific Science Center, Seattle) and “ The Physics of the Pump Organ ” by Kristina Knupp.
 

Bibliography
Berg, Richard E. and David G. Stork. The Physics of Sound. Englewood Cliffs: Prentice Hall Inc., 1982.
Fletcher, Neville H. and Thomas D. Rossing. The Physics of Musical Instruments . New York: Springer-Verlag, 1991.
Roederer, Juan G. Introduction to the Physics and Psychophysics of Music . London: The English Universities Press Ltd., 1973.
Rossing, Thorras D., ed. Musical Acoustics. College Park: American Association of Physics Teachers, 1988.
Rossing, Thomas D. The Science of Sound. Reading: Addison-Wesley Publishing Cc., 1990.

Revised:  12 February 2003