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Additional Waveforms:
More complicated tones can be represented by a Fourier series,
a sum of pure tones whose frequencies are integer multiples (harmonics) of a
fundamental frequency, wo:
x(t) = a1 cos(wot
+ q1)
+ a2 cos(2wot
+ q2)
+ a3 cos(3wot
+ q3)
+ ...
The pitch of the tone is related to wo. The higher harmonics affect the 'richness'
or 'harshness' of the tone. Compare the sound of the following tones, all with the fundamental
frequency 400 Hz. The frequency components making up these tones are shown by the
amplitude spectrum of the tone, which is a plot of the coefficients
ak vs. k.
Each musical instrument has its own amplitude spectrum.
This is primarily what gives each instrument its unique sound.
Compare the tones of an oboe and a clarinet by clicking on the
corresponding plots below.
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400 Hz Sine Wave
400 Hz Square Wave
400 Hz Sawtooth Wave
400 Hz Triangle Wave