Upcoming Classes Thursday, Oct. 18 th The Ear and the Brain Assignment due: * Read “Brass Instruments”, Measured Tones: The Interplay of Physics and Music, I. Johnston, Pages Tuesday, Oct. 23 rd Design at the Nexus Special Guest: Corbett Griffith, Designer/Engineer/Artist Assignment due: * None

Upcoming Deadlines Tuesday, October 16 th Outline of second oral presentation or written paper Tuesday, November 6 th Second Set of Oral Presentations Second term paper (if not presenting)

Oral Presentations (II) The following persons will give oral presentations on Tuesday, November 6 th : 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. 16 th 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. 15 th – 18 th ). 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 string Drumhead

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. Drumhead Same 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 c 2 = a 2 + b 2

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. C5C4C5C4

Perfect Fifth If the second string is 2 / 3 rd the length then the two notes are said to be “a fifth apart.” G4C4G4C4 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 Hz277 Hz294 Hz311 Hz330 Hz349 Hz F#G (So)G#A (La)A#B (Ti) 370 Hz392 Hz415 Hz440 Hz466 Hz494 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 12 th 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