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Re: sympathetic resonances



This discussion is getting to the electrical engineer in me. Resonance
frequencies of an oscillator are the frequencies at which they naturally
oscillate. Whether they oscillate or not depends on the driving force. If
the driving force contains components of those natural resonance
frequencies, it will cause the device to oscillate. If this driving force
is at the fundamental frequency or some harmonic of that frequency, it is
those modes will be excited. The example of setting a piano string into
vibration by releasing the damper and humming at its natural frequency was
given. Another more curious demonstration with a piano is to hold down but
don't strike (removing the damper) one key then go up one octave and strike
that key. When you release it, the lower frequency key will be oscillation
at the higher one's frequency. In this case the driving force is picking
the frequencies to be excited. There are some other neat variations on this
theme.
Rabi on first seeing the British magnetron? commented "it is just a
whistle" and MIT's Radiation Laboratory set to work finding out how
whistles work. They work by you generating a source of "white noise" like
blowing across the top of the pop bottle. The bottle then selects out the
components of the noise that correspond to its natural resonance
frequencies. Those frequencies that are being driven by the noise are
resonances that become much louder. Which resonances and how loud they
become depends on the frequency spectrum of the noise source and the
relative amplitudes of its components within the source. String
instruments are not plucked or bowed at the center but off to one side to
excite not only the fundamental frequency but their harmonics as well. It
is the harmonics that help make an instrument sound the way it does.
Frank Crawford's sound pipe is excited by twirling the corrugated plastic
tube. At different speeds different harmonics are excited because of the
change in the spectrum of the noise generated by the corrugations but the
length of the tube selects the resonance frequencies. A radio receiver
amplifies the radio noise that is at the resonance frequency it is tuned
to. If not signal is present in the noise at that frequency nothing is
received.
You can use a resonance device to oscillate itself by feeding some of the
output oscillations back into the device in phases with its vibrations.
Such a device is called appropriately an oscillator. The trick in such a
system is to feed back only enough signal to overcome the natural damping,
otherwise your device will go the way of the bridge. Most oscillators have
some kind of limiting built into them so they don't self destruct.

Gary





Gary Karshner

St. Mary's University
San Antonio, Texas
KARSHNER@STMARYTX.EDU