PH 105 Dr. Cecilia Vogel Lecture 12

OUTLINE  Timbre review  Spectrum  Fourier Synthesis  harmonics and periodicity  Fourier Analysis  Timbre and graphs:  Time graph  Spectrum graph  Spectrogram

Timbre  Timbre or tone quality  depends primarily on   A pure tone has a  tuning fork  complex tones have  vowel sounds, “noisemaker”, links on web  noise  H sound

More on Complex Tones  Sometimes a complex tone sounds like   if the ______of the wave  other times,  if one ____ is strong and the rest  yet other times, as  or a  if several frequencies are strong.  Depends on

Spectrum  Timbre of tone  depends strongly on waveform.  Timbre of tone  depends strongly on spectrum.  Waveform can be built from  pure tones (sine waves) of  Spectrum of wave is  which  and the

Pure tones  Consider two pure tones: 66.7 Hz and 200 Hz

Synthesize Waveforms  Add the two pure tones with

Fourier Synthesis  Fourier Synthesis means  to create a waveform  by adding  each with the appropriate

Synthesize Square Wave  To create a square wave:  Start with __________ frequency  Add in only ___ harmonics  The amplitude of the n th harmonic should be 1/n

Synthesize Square Wave Start with fundamental ____ Add 3rd harmonic, _____ at Including _____ at ___ amp, thru _____ at ___ amp Approximates

Synthesis with Harmonics  If you take a fundamental tone  and add only   then the synthesized wave will have the same frequency as  As with the square wave.

Periodicity Example  Suppose fundamental frequency is 0.1 Hz  then the period is  Harmonics also repeat:  frequency of 2 nd harmonic:  the period is _____, repeats after ____,  repeats again after  frequency of 10 th harmonic: 1.0 Hz,  repeats after ____; repeats  All harmonics are repeating after 10 s  The wave has a period of 10 s, f= __

Another Example  Suppose a waveform is synthesized from the following frequencies   What will be the frequency of the resulting wave?  One repeats every___, another every ___, another every ___.  How long before all will be repeating?  Wave is made up of harmonics of  so wave frequency is

Missing Fundamental  If the spectrum of a sound wave contains only multiples of f 1,   the frequency (and usually the pitch) of the sound   You hear a frequency that is not even in the spectrum of the sound.

Fourier Analysis  Fourier Synthesis meant from the spectrum, build the waveform.  Fourier Analysis means  from the waveform,  Let’s let the computer do it.  This yields a spectrum graph or FFT graph  Amplitude vs  From a spectrum graph, can determine  

Graphs  Compare violin and tuning fork  Amanda Young, Spring 2000  Time graphs and spectrum graphs  pitch,    timbre,    s /fork-violin-2.html s /fork-violin-2.html

Summary  Fourier Synthesis and Analysis  complex wave built from pure sine waves  Periodicity of wave  = period of fundamental  Time graph  pressure vs time  period easily seen (sometimes)  amplitude and time variations clear  Spectrum graph  amplitude vs frequency  spectrum easily seen  time variation unknown