Upcoming Classes
Thursday, Oct. 18th
The Ear and the Brain
Assignment due:
* Read “Brass Instruments”, Measured Tones: The Interplay of
Physics and Music, I. Johnston, Pages 40-60
Tuesday, Oct. 23rd
Design at the Nexus
Special Guest: Corbett Griffith, Designer/Engineer/Artist
Assignment due:
* None
Upcoming Deadlines
Tuesday, October 16th
Outline of second oral presentation or
written paper
Tuesday, November 6th
Second Set of Oral Presentations
Second term paper (if not presenting)
Oral Presentations (II)
The following persons will give oral presentations
on Tuesday, November 6th :
• Luttrell,Katherine
• Macdonald,Keith
• McDonald,Kathleen
• Mendoza,Jazmin
• Nguyen,Jennifer
• Nguyen,Linda
For everyone else, term paper is due on that date.
Extra Credit: SF Museum of Art
Visit San Francisco Museum of Modern Art and
see Abstract Expressionist paintings.
Turn in your ticket receipt ($7 for students). Worth
one homework assignment; deadline is Oct. 16th
Guardians of the Secret, Jackson Pollock, 1943
Extra Credit: San Jose Ballet
See a performance of San Jose Ballet in San Jose
Center for Performing Arts (Nov. 15th – 18th ).
Turn in your ticket receipt. Worth one homework
assignment or three quiz/participation credits.
Ramon Moreno in CARMINA BURANA
Good Vibrations &
Bad Oscillations
Origin of Sound
Sound is produced by
the vibrations of
material objects.
Drumhead
Guitar string
Tuning fork
Vibrations & Oscillations
Vibrations and oscillations are common
mechanical phenomena.
Vibrations of a
diving board
Oscillating
motion of a
mass on a
spring
Slower vibrations are not audible but are easier to measure and analyze
Amplitude
The distance
from the rest
position is the
amplitude of
oscillation.
Amplitude
Period
Time required for
a full oscillation
(one round trip)
is called the
period of
oscillation.
Period of this pendulum is about
one second per oscillation
Musical Notes
A musical note has four characteristics:
• Loudness
• Pitch (such as soprano versus alto)
• Duration
• Timbre (such as piano versus violin)
Let’s investigate the physical properties
underlying these four characteristics.
Loudness & Amplitude
The loudness of a note is an indication
of the amplitude of the sound.
The harder you strike a tuning fork, the larger the
amplitude of the oscillation and the louder the
sound made by the tuning fork.
Same is true for a plucking
guitar string, banging a drum, or
blowing a whistle.
Drumhead
Vibrations & Pitch
The faster the vibrations (shorter the
period), the higher the pitch of the
musical note produced.
The relationship
between the pitch of
a note and the
corresponding
vibration is given by
the frequency.
Frequency
Frequency is the inverse of the period,
(Frequency) =
1
(Period)
For example, for a period of 2 seconds per
oscillation, the frequency is ½ oscillation
per second or ½ Hertz.
1 Hertz = 1 oscillation per second
Pythagoras
Pythagoras of Samos (582 BC–
507 BC), was a Greek
mathematician, scientist, and
philosopher, best known for the
Pythagorean theorem:
c2 = a2 + b2
The square of the hypotenuse
(diagonal) equals the sum of the
squares of the sides of a triangle
Pythagoras & Music
Pythagoras discovered
that different musical
notes were related by
mathematical ratios,
such as the ratios of
lengths or sizes in
musical instruments or
even in simple objects.
Octave
The note produced by two strings, one half
the length of the other, sounded similar.
In Western music these two notes are said
to be an octave apart.
Men and women
typically sing an
octave apart.
C5
C4
Sing “Some-where over the rainbow…”
Perfect Fifth
If the second string is 2/3rd the length then
the two notes are said to be “a fifth apart.”
Typical separation
between tenor and
bass or soprano
and alto.
G4
C4
Sing “Twin-kle, twin-kle little star…”
Notes and Powers of Two
An octave has 12 steps and going up an
octave doubles the frequency.
The frequency of “Concert A” is 440 Hz.
The frequency of other notes is
(Frequency) = 2(steps)/12 x (440 Hz)
= (1.09) (steps) x (440 Hz)
counting number of steps from Concert A
Notes & Frequencies
Middle C
C (Do) C#
D (Re) D#
E (Mi)
F (Fa)
262 Hz 277 Hz 294 Hz 311 Hz 330 Hz 349 Hz
Concert A
F#
G (So) G#
A (La)
A#
B (Ti)
370 Hz 392 Hz 415 Hz 440 Hz 466 Hz 494 Hz
For example, Middle C is 9 steps below Concert A so it is
(Frequency) = 2(-9)/12 x (440) = 2(-0.75) x (440) = 262 Hz
Guitar Frets
Each fret decreases the string length by about 9%, which is one step.
At the 12th fret the string length is half the open length (i.e., one octave)
Piano Keyboard (Upper Half)
Duration of a Note
Duration is the amount of time from the
beginning to the end of the note.
The tempo set by the
composer establishes the
conversion between the
measure of a note (whole
note, half note, etc.) and the
number of milliseconds of time
for that note’s duration.
Traditional metronome is a
wind-up pendulum clock.
Timbre
Spectrum of frequencies produced by a musical
instrument gives it its unique voice, its timbre.
The frequencies produced by
a flute playing an A (slightly
flat) show that the
fundamental (436 Hz) and the
harmonic (872 Hz) have
almost the same amplitude.
The spectrum of a tuning fork
would have only a single peak
at the fundamental.
Natural Frequencies
Metal wrench and
wooden bat sound
very different when
dropped to the
floor.
Different materials
and shapes vibrate
at their own natural
frequencies.
Forced Vibrations
Vibrating guitar strings force the vibration of the
guitar’s body, producing most of the sound.
553 Hz
731 Hz
Circular rings indicate where the
surface is vibrating up and down
Demo: Tuning Fork & Sound Box
Tuning fork by itself is not
very loud.
Sound is much louder if it
is held against a sound
box, such as the body
of a guitar or any similar
rigid surface.
The tuning fork forces the
surface into oscillation
at the same frequency.
Resonance
Resonance occurs when forced vibrations match an
object’s natural frequency.
Oscillations grow in amplitude due to synchronized
transfer of energy into the vibrating object.
Acoustic Resonance
Sound at an object’s natural frequency
can produce resonant vibrations.
If the amplitude of the sound is
sufficiently large, resonant
vibrations can shatter a wine glass.
As shown by Myth Busters, this
may even be achieved by
exceptionally powerful singers (and
by average singers using electronic
amplifiers).
Tacoma Narrows Bridge
In 1940, the first Tacoma Narrows bridge
was destroyed by resonance.
First Bridge
Second Bridge
Movie: Tacoma Narrows Bridge
Next Lecture
Waves &
Sound
Remember:
Assignment due:
Read “Brass Instruments”,
Measured Tones:
The Interplay of Physics and Music,
I. Johnston, Pages 40-60