Ed Schweber (edschweb@ix.netcom.com)
Physics Teacher at The Solomon Schechter Day School, West Orange, NJ
To obtain free resources for creative physics teachers visit: http://www.physicsweb.com
Hi All:
If a guitar string is deformed and then released, my very unreliable
intuition tells my that the relative amplitudes of the Fourrier components
of the deformed shape of the string should also be the relative amplitudes
of the harmonics in which the string subsequently vibrates and that the
different timbres of a guitar and banjo should then be due to which of these
harmonics create resonances in the rest of the instrument.
But I also recall reading somewhere that the initial waveform of the
sound wave produced after a string is plucked is different than the waveform
that evolves after a short time interval and that what we hear as the
difference between a banjo and guitar playing the same note is really due to
the differences in this initial waveform. According to what I read, if the
initial waveforms in each note of a recording of a guitar are electronically
replaced by the corresponding waveforms from a banjo (but the subsequent
"steady state" waveforms are left alone) the recording will sound more
banjo-like than guitar-like. But if this is true, it would seem to be at
odds with my intuition since that idea would seem to be unable to account
for the any evolution in the waveforms.
Is there any connection between the harmonics and the Fourrier components
of the original shape? any insight would be appreciated.