Page 12 - Vibrations
P. 12
Many of the notes on the piano have two and some three
strings.
They are not tuned to the same frequency. There is a
slight difference between them – a fraction of a Hz.
The piano tuner listens for these beat frequencies.
What happens when the frequencies are harmonically
related?
By this we mean, the frequencies are integers of each
other, 500 Hz, 1000 Hz, 1500 Hz …
Fourier Series
Jean-Baptiste Joseph Fourier French:
21 March 1768 – 16 May 1830.
He was one of Napoleon’s Generals,
but he was a better mathematician
than an army officer.
He stated that all periodic waveforms
can be constructed by the synthesis of
a fundamental frequency and its harmonics.
=∞
0
() = + ∑ [ sin( ) + cos( )]
2
=1
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