Lab 6: Fourier Analysis A steady musical tone from an instrument
or a voice has, in most cases, quite a complicated wave shape.
The oscillations repeat themselves f times a second, where f is
called the fundamental frequency. We have learned that f is
related to the pitch of the tone. Tones played on different
instruments sound different — musicians say that the tones have
different timbre or different tone color. How does one describe
wave shape? In Fourier Analysis we represent the complex wave
shape as a sum of sine waves (or a sum of “partials”), each of a
different amplitude. If the wave shape is periodic, the
frequencies of the partials are multiples of the fundamental
frequency and are called the “harmonics” of the tone being
played. If the frequency of the musical tone is, for example,
200 Hz, the fundamental (also called the “first harmonic”) has a
frequency of 200 Hz; the second harmonic (also called the first
overtone) has a frequency of 400 Hz; the third harmonic (or
second overtone) has a frequen