1 / 13

# Chapter 8 (Hall) - PowerPoint PPT Presentation

Chapter 8 (Hall). Sound Spectra. Introduction. Question : When you hear the music “Danny Boy”, what lets you distinguish between a trumpet and a flute? Answer : Each periodic waveform has its corresponding spectrum , which determines the timbre , or tone quality of the sound.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Chapter 8 (Hall)' - keelie-nichols

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Chapter 8 (Hall)

Sound Spectra

PHY 1071

• Question: When you hear the music “Danny Boy”, what lets you distinguish between a trumpet and a flute?

• Answer: Each periodic waveform has its corresponding spectrum, which determines the timbre, or tone quality of the sound.

PHY 1071

Flute C Note

Trumpet C Note

PHY 1071

• The harmonic series

• Periodic waves and Fourier spectra

• Fourier spectrum

• Fourier components

• Fourier synthesis

• Fourier analysis

PHY 1071

• An example of a harmonic series: f1 = 110 Hz, f2 = 220 Hz, f3 = 330 Hz, … f10 = 1100 Hz,…so on.

• Harmonic series: A Harmonic series contains a group of frequenciesthat are based on a single frequency, f1, which is called the fundamental frequency. The frequencies of the other members are simple multiples of the fundamental.

• fn = nf1, n = 1, 2, 3,…

• f1: the fundamental frequency; f2: the 2nd harmonic; f3: the 3rd harmonic, … and so on.

PHY 1071

• (a) Sine wave (b) Square wave (c-d) Pulse wave (e) Triangular wave (f-h) Saw-tooth wave

• What is the simplest of all wave forms?

• Answer: Sine waves. They are the “building blocks” for other more complex wave forms.

PHY 1071

• (1) Take simple periodic sine waves and put them together to form a more complex wave.

• (2) Take a complex periodic wave and break it down into simple sine wave components.

PHY 1071

f1=110 Hz

f = f1= 110 Hz

f2=220 Hz

Combination of sine waves

• Any set of sine waves whose frequencies belong to a harmonic series will combine to make a periodic complex wave, whose repetition frequency is that of the series fundamental.

+

PHY 1071

• In general, for a set of sine waves whose frequencies do not belong to a harmonic series, the combined wave will be non-periodic.

PHY 1071

• Any periodic waveform of period T may be built from a set of sine waves whose frequencies form a harmonic series with fundamental f1 = 1/T. Each sine wave must have just the right amplitude and relative phase, and those can be determined from the shape of the complex waveform.

PHY 1071

Recipe for building a square wave

PHY 1071

• Fourier spectrum: The recipe of sine wave amplitudes involved in a complex wave.

• Fourier components: Each sine wave ingredient is called a Fourier component.

• Fourier synthesis: Putting sine waves together to make complex waves.

• Fourier analysis: Taking complex waves apart into their sine wave components.

Fourier spectrum of a square wave

PHY 1071

• Ch. 8 (Hall), P. 146, Exercises: #1, 2.

PHY 1071