Dr. Jie Zou PHY 1071 1
Chapter 8 (Hall)
Sound Spectra
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Sound Spectra - Physics of Sound and Music - Lecture Slides | PHY 1071, Study notes of Physics
Material Type: Notes; Professor: Zou; Class: Physics of Sound and Music; Subject: Physics; University: Eastern Illinois University; Term: Unknown 1989;
Typology: Study notes
Pre 2010
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Dr. Jie Zou
PHY 1071
Chapter 8 (Hall)
Sound Spectra
Dr. Jie Zou
PHY 1071
Introduction
Question: When you hear the music “DannyBoy”, what lets you distinguish between atrumpet and a flute?
Answer: Each periodic waveform has itscorresponding
spectrum
, which determines
the
timbre
, or tone quality of the sound.
Dr. Jie Zou
PHY 1071
Outline^
The harmonic series
Prototype steady tones
Periodic waves and Fourier spectra
Fourier spectrum
Fourier components
Fourier synthesis
Fourier analysis
Dr. Jie Zou
PHY 1071
The harmonic series^
An example of a harmonic series: f
1
= 110 Hz, f
2
220 Hz, f
3
= 330 Hz, … f
10
= 1100 Hz,…so on.
Harmonic series
: A Harmonic series contains a
group of frequencies that are based on a singlefrequency, f
1
, which is called the fundamental
frequency. The frequencies of the other members aresimple multiples of the fundamental.
f n = n × f 1 , n = 1, 2, 3,… f 1 : the fundamental frequency; f 2 : the 2 nd harmonic; f 3 : the 3 rd harmonic, … and so on.
Dr. Jie Zou
PHY 1071
Two things to show^
(1) Take simple periodic sine waves andput them together to form a morecomplex wave.
(2) Take a complex periodic wave andbreak it down into simple sine wavecomponents.
Dr. Jie Zou
PHY 1071
f = f 1 = 110 Hz
Combination of sine waves
f 2 =220 Hz f 1 =110 Hz T
Any set of sine waveswhose frequenciesbelong to a harmonicseries will combine tomake a periodiccomplex wave,whose repetitionfrequency is that ofthe seriesfundamental.
Dr. Jie Zou
PHY 1071
Breaking a periodic complexwave^
Any periodic waveform of period T maybe
built from a set of sine waves whose
frequencies form a harmonic series withfundamental f
1
= 1/T. Each sine wave
must have just the right amplitude,which can be determined from theshape of the complex waveform.
Dr. Jie Zou
PHY 1071
Recipe for building a squarewave
After 200 selected sinewaves added together
Dr. Jie Zou