Wrong, Arnie. You don't have a ****ing clue.
The sum and idfference terms arise from _mixing_, which requires some non-
linearity. Just adding the two sinewaves gives you two sinewaves.
Correct. Linear systems do NOT produce combination tones.
I think what usually causes this low frequency vibration is a little different.
Each of the drives is slightly out of balance, and running at slightly different
rotational speed. At some point the out of balance condition on both drives is
adding to make a larger amplitude vibration, and later it tends to cancel making
the net vibration less. Your suggestions for ways to reduce the problem should do
the trick for the OP.
Any book on physics/psychology of hearing explains the difference between
linear and non-linear superposition. Here is a good one:
http://ccrma.stanford.edu/courses/150-2001/combination_tones.html
Linear Superposition
a.. The response of a linear system to multiple inputs is just the sum of the individual
responses.
b.. N different frequency inputs will produce a response given by the same N frequencies (with
the possibility of total cancellation of same-frequency components).
c.. Two simple harmonic waveforms of the same frequency will add to produce a single harmonic
waveform of the same frequency. The resulting amplitude and phase will depend on the individual
amplitudes and phases of the two waveforms.
Beats
a.. When two pure tones of slightly different frequency are superposed, our ears perceive audible
beats at a rate given by the difference of the two frequencies.
b.. Beats are heard as a pulsation in the loudness of a tone at the ``average'' frequency .
c.. When the difference frequency exceeds about 15 Hz, the beat sensation disappears and a
characteristic roughness of sound appears.
d.. As the difference frequency is increased further, a point is reached at which the ``fused''
tone at the average frequency gives way to two tones, though still with roughness. At this point,
the resonance regions on the basilar membrane are sufficiently separated to produce two distinct
pitch signals, but these regions still overlap to produce roughness.
e.. Finally, when the difference frequency exceeds the critical bandwidth, the roughness
disappears completely.
Combination Tones
a.. When two tones are sounded together, a tone of lower frequency is frequently heard. Such a
tone is called a Tartini tone or combination tone.
b.. The most commonly heard combination tone occurs at a frequency (or ).
c.. Other combination tones can occur at frequencies given by , , ..., , though these are much
less common.
d.. Combination tones expose nonlinearities in our auditory system.
Other Nonlinear Effects
a.. A single, loud tone of frequency should produce additional pitch sensations at , etc. These
are called aural harmonics.
b.. A nonlinear mechanism in the ear should result in summation, as well as difference, tones.
Perception of such higher frequency tones, however, has yet to be adequately demonstrated.
Here is another book:
http://www.lifesci.sussex.ac.uk/home/Chris_Darwin/Perception/Lecture_Notes/Hearing_Index.html
Essential quote from Intro: "A linear system can only output frequencies that are
present on the input, non-linear systems always add extra frequency components"
