1 / 13

Chapter 8 (Hall)

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.

keelie-nichols
Download Presentation

Chapter 8 (Hall)

An Image/Link below is provided (as is) to download presentation 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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 8 (Hall) Sound Spectra PHY 1071

  2. 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. PHY 1071

  3. Waveforms and spectra of a flute and a trumpet Flute C Note Trumpet C Note PHY 1071

  4. Outline • The harmonic series • Prototype steady tones • Periodic waves and Fourier spectra • Fourier spectrum • Fourier components • Fourier synthesis • Fourier analysis PHY 1071

  5. The harmonic series • 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

  6. Prototype of periodic steady tones • (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

  7. Two things to show • (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

  8. T 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

  9. Combination of sine waves (cont.) • 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

  10. Breaking a periodic complex wave • 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

  11. After 200 selected sine waves added together Recipe for building a square wave … PHY 1071

  12. Fourier spectrum • 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

  13. Homework • Ch. 8 (Hall), P. 146, Exercises: #1, 2. PHY 1071

More Related