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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

Uploaded on 08/18/2009

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Dr. Jie Zou PHY 1071 1
Chapter 8 (Hall)
Sound Spectra
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Download Sound Spectra - Physics of Sound and Music - Lecture Slides | PHY 1071 and more Study notes Physics in PDF only on Docsity!

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

PHY 1071

Homework^ „

Ch. 8 (Hall), P. 146,

Exercises