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The Sounds of Science

Physics is Phun

March 2007

Reference book:

The Physics of Sound, 3rd edition (2005)

by Richard E. Berg and David G. Stork

published byPearson/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, 2f, 3f, 4f, ... --from “Wikipedia”

Fourier SynthesisSawtooth wave

Fourier SynthesisPulse train wave

Fourier SynthesisTriangular wave

Fourier SynthesisSquare wave

Fourier Analysisor

Spectrum Analysis

Sine Wave Spectrum

Sawtooth Wave Spectrum

Pulse Train Spectrum

Triangular Wave Spectrum

Square Wave Spectrum

Analysis of

Musical Sounds

Fourier Analysisof

Sounds ofMusical Instruments

Recorder Wave and Spectrum

Violin Wave and Spectrum

Crumhorn Wave and Spectrum

Clarinet Wave and Spectrum

Factors in Tone Quality1. 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)

Frequency:

f1 = 500 Hz

f3 = 1500 Hz

Vocal range:

150-850 Hz

500-2500 Hz

Mode:

Simple formant model

Origin of Vocal Formants(~17.5 cm closed tube)

Frequency:

f1 = 500 Hz

f3 = 1500 Hz

Vocal range:

150-850 Hz

500-2500 Hz

Mode:

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

He SF6

M/Mair 1/7 4.6

Vs/S 2.6 0.5

The EndSee you next time!

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