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,LindaFor 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.

Tuning fork

Guitar stringDrumhead

Vibrations & Oscillations

Vibrations and oscillations are common mechanical phenomena.

Oscillating motion of a mass on a spring

Vibrations of a diving board

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.

DrumheadSame is true for a plucking guitar string, banging a drum, or blowing a whistle.

The harder you strike a tuning fork, the larger the amplitude of the oscillation and the louder the sound made by the tuning fork.

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) =

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

(Period)

1

Pythagoras

Pythagoras of Samos (582 BC–507 BC), was a Greek mathematician, scientist, and philosopher, best known for the Pythagorean theorem:

The square of the hypotenuse (diagonal) equals the sum of the squares of the sides of a triangle

c2 = a2 + b2

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.

Sing “Some-where over the rainbow…”

Men and women typically sing an octave apart.

C5

C4

Perfect Fifth

If the second string is 2/3rd the length then the

two notes are said to be “a fifth apart.”

G4

C4

Typical separation between tenor and bass or soprano and alto.

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

C (Do) C# D (Re) D# E (Mi) F (Fa)

262 Hz 277 Hz 294 Hz 311 Hz 330 Hz 349 Hz

F# G (So) G# A (La) A# B (Ti)

370 Hz 392 Hz 415 Hz 440 Hz 466 Hz 494 Hz

Middle C

Concert A

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.

ResonanceResonance 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