Re: More dead spots.
- From: Steve <smcyr@xxxxxxxxxxxxxxxxxx>
- Date: Wed, 24 Oct 2007 22:49:43 -0700
I was temped to ask how you know that a tree falling in the forest with no
one to hear it makes a sound, but I'll offer this possibility instead:
When the end of a string is fixed, the displacement of the string at that
end must be zero. A transverse wave travelling along the string towards a
fixed end will be reflected in the opposite direction. When a string is
fixed at both ends, two waves travelling in opposite directions simply
bounce back and forth between the ends.
The vibrational behavior of the string depends on the frequency (and
wavelenth) of the waves reflecting back and forth from the ends.
A string which is fixed at both ends will exhibit strong vibrational
response only at the resonance frequncies...
...is the speed of transverse mechanical waves on the string, L is the
string length, and n is an integer. At any other frequencies, the string
will not vibrate with any significant amplitude. The resonance frequencies
of the fixed-fixed string are harmonics (integer multiples) of the
fundamental frequency (n=1).
The vibrational pattern (mode shape) of the string at resonance will have
This equation represents a standing wave. There will be locations on the
string which undergo maximum displacement (antinodes) and locations which to
not move at all (nodes). In fact, the string may be touched at a node
without altering the string vibration.
Your analysis assumes that the ends of the string are fixed (at the nut [or fret], and at the saddle) but this is not the case. Both the nut (or fret) and saddle can move and resonate (or not resonate) since they are all parts of the complex system that is the bass - which is not perfectly rigid, and has vibrational and resonant characteristics of its own. The dead spot we are talking about is the result of the bass's resonant and damping characteristics interacting with the vibrational behavior of the string. Ideally, we want a bass that bleeds off (dampens) only a small amount of the string's energy, in a manner that is independent of the frequency of vibration. If the bass dampens a lot of that energy rapidly for a given note on a given string, we call that a dead spot.
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