On Sat, 25 May 2002, Russell McMahon wrote:

>> >I don't get what the beat freq has to do with this. A beat shouldn't be
>> >able to excite a resonance at the beat freq, unless there are significant
>> >nonlinear mixing effects going on.
>>
>> I don't know either but windows usually don't close perfectly and have
>> some play, especially large tall church windows. Maybe this was the
>> 'diode'. Anyway they took a few seconds to start 'singing'. I'm pretty
>> sure damage would have occured before too long (I did not intend to do any
>> damage - I was quite scared in fact).
>
>I'm not sure that the electrical analogue applies fully here. Unlike EM
>waves we are certain that there IS an "ether" in this case - the air is the
>medium that the waves are produced in. When two such waves interact they are
>represented by real pressure phenomena in the gas and "mixing" occurs at all
>points.

My experience with mechanical harmonic oscillators is that nonlinear
events in the course of the motion cause harmonics. Example is guitar
string and incorrectly fastened fret (gives 'metal' sound liked by some =
lots of harmonics of the fundamental and some others caused by the
separately vibrating two sides of the chord - the metal fret becomes a
forced null for half the period of the fundamental).  Also two crystal
glasses pinged very close together so they touch will make weird sounds
(harmonics again).

In general a harmonic oscillator that can impact elastically on something
(by elastic I do not mean rubber - rather marble or solid steel) will make
a lot of harmonics. Think of the noise produced by fans, washing machines,
motors etc when their elastic mountings fail and allow them to touch their
bases intermittently.

>In the case of my locomotive beating experience (which occurred
>intermittently but on numerous occasions over the years that I lived there)
>the effect was extremely real and manifestly repeatable. While I am not
>CERTAIN that the effect was in fact caused by the two engines running side
>by side at nominally identical rpm I can not think of a more probable
>explanation. This only occurred in the early morning before (winter) dawn
>and only for a limited period in each case. The "sound" levels were high and
>they came from the shunting yard. I can imagine that the workers may even
>have worked hard to produce the effect by careful idle speed adjustment :-).

Peter

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