POS_18 - Physics of Sound Lecture 18 1. Fourier analysis...

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Physics of Sound Lecture 18 1. Fourier analysis and synthesis of waves. 2. Fourier Analysis of tones. 3. Tone quality.
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Fourier Analysis • Mathematically, any sound can be analyzed in terms of (taken apart – seen as the linear superposition of) pure constant tones. They can must be added with the correct amplitude and phase, but in this way you can make any sound.
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The trace on the bottom is the sum of all the cosine waves above it.
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Two representations Time domain Frequency domain
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Spectrogram is in the middle
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Fourier analysis of tones • Any periodic wave with period T can be made out of a superposition of all the (open tube) overtones from the series with fundamental frequency f 1 =1/T; A (t)=a 1 *sin(2 π t/T+ φ 1 )+a 2 *sin(4 π t/T+ φ 2 )+ a 3 *sin(6 π t/T+ φ 3 )+a 4 *sin(8 π t/T+ φ 4 )+. .
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Classic method of analysis the Helmholtz oscillator Not a standing wave!
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Descriptions of tone quality • The first way to describe tone quality is by overtone composition. For a strictly
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POS_18 - Physics of Sound Lecture 18 1. Fourier analysis...

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