WELCOME to Physics is Phun Please be Seated

WELCOME to Physics is Phun

Please be Seated

Physics Lecture-Demonstration Web Site Summer Programs for Youth Physics Olympics Physics Question of the Week

The Sounds of Science Physics is Phun March 2007

Reference book: The Physics of Sound, rd 3 edition (2005) by Richard E. Berg and David G. Stork published by Pearson/Prentice-Hall

The Overtone Series

Standing waves in a string

The Overtone Series

Standing waves in air columns

The Overtone Series

Standard electronic wave forms • • • Sine wave Sawtooth wave Pulse train Triangular wave Square wave

Fourier’s Theorem: Jean Baptiste Joseph Fourier (1768 - 1830) Any physical function that varies periodically with time with a frequency f can be expressed as a superposition of sinusoidal components of frequencies: f, 2 f, 3 f, 4 f, . . . --from “Wikipedia”

Fourier Synthesis Sawtooth wave

Fourier Synthesis Pulse train wave

Fourier Synthesis Triangular wave

Fourier Synthesis Square wave

Fourier Analysis or Spectrum Analysis

Sine Wave Spectrum

Sawtooth Wave Spectrum

Pulse Train Spectrum

Triangular Wave Spectrum

Square Wave Spectrum

Analysis of Musical Sounds

Fourier Analysis of Sounds of Musical Instruments

Recorder Wave and Spectrum

Violin Wave and Spectrum

Crumhorn Wave and Spectrum

Clarinet Wave and Spectrum

Factors in Tone Quality 1. Amplitudes of harmonics 2. Attack and decay transients 3. Inharmonicities 4. Formants 5. Vibrato 6. Chorus effect

The Singing Formant

Origin of Vocal Formants (~17. 5 cm closed tube) Mode: Frequency: Vocal range: f 1 = 500 Hz 150 -850 Hz f 3 = 1500 Hz 500 -2500 Hz

Simple formant model

Origin of Vocal Formants (~17. 5 cm closed tube) Mode: Frequency: Vocal range: f 1 = 500 Hz 150 -850 Hz f 3 = 1500 Hz 500 -2500 Hz

Vowel formant production Source: http: //hyperphysics. phy-astr. gsu. edu/hbase/hframe. html

Vowel Formant Frequencies

Sound Spectrograms

Vocal formants for vowel sounds

Voice and Synthesizer “Wow”

Vocal Spectrograms

Computerized Speech Laboratory Courtesy of Kay Elemetrics Corp.

Helium Voice Singing frequency remains the same (vibration of vocal folds) Formant frequencies rise because She >> Sair Why?

Vowel formant production Source: http: //hyperphysics. phy-astr. gsu. edu/hbase/hframe. html

Speed of Sound in Helium and Sulfur Hexafluoride M/Mair He 1/7 SF 6 4. 6 Vs/S 2. 6 0. 5

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