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Re: OT-fundamentals in sound (was singing bowls)



--- "Ryan D. Supak" <rdsupak@hoover-keith.com> wrote:
> i am an acoustics engineer (honest, check hoover-keith.com!)
> 
> firstly, anything can theoretically generate any frequency (e.g. i
> can
> generate a 10 hz tone by tapping my fingers 10 times per second on a
> paper plate.)
> 
> ****ultra-simplified resonance theory****
> 
> however, any resonating object can only have two of these three
> qualities:
> 1) small size
> 2) high efficiency
> 3) large low frequency emission
> 
> thus, a small bowl *can* generate, say, a 35Hz fundamental, albeit
> extremely inefficiently (assuming modern materials, 12.5 PSI, sea
> level,
> typical acoustic space, etc...)
Ryan,
I basically agree with what you say here.  The terms small, high, and
large are very general terms, as you said these are simplified
principles.  

I encountered this trade-off between smallness, efficiency, low freq
output with the Thiele/Small loudspeaker enclosure design principles. 
The point is that there are trade-offs between these 3 metrics.  In the
Thiele/Small world the notions of small, efficient, and low freq output
are looked at in a relative, not absolute way. That is, if you have box
design of X cubic feet, and you make it smaller, you will diminish one
of the other 2 parameters (you will either loose efficiency, or low
frequency output, or some of both).  

So how small a bowl is too small to be (physically) able to create the
low freq, loud (vague terms) sound we hear from the bowls, with the
amount of energy we apply to the bowls?

Is a 15" loudspeaker cone small?  The 20" bowls vibrating surface is
larger than the speaker size that is commonly used for generating loud,
low freq.  I have casually mapped the vibrating surface and it seems to
be virtually the entire sides of the bowl, down to the start of the
base.  The bowl is small, but the radiating surface of the bowl seems
large to me.  But small and large are relative terms, aren't they?

Regarding efficiency, I cannot say how efficient the bowls are.  As you
play them you constantly put energy into them.  I make no claims for
the bowls efficiency, but they could be inefficient (and per stated
principles) and still be loud and low freq.  It tires me to play them
for very long, but I'm not sure how to quantify the energy I put into
the bowl from the playing (how efficient is the energy transfer from my
hand to the stick to the bowls edge?).  A single strike to the bowl
will excite it at the low fundamental, if you hit it in the right area.

Anyway, I am very curious about what is happening, and sorry if this
thread is wearing thin for some of you.  I find the singing bowls
fascinating and fun, and it is my nature to try and figure out how
things work, especially sound (I too am an engineer, but acoustics are
only a part of my job with disk drive design).
I'll shut up now, and see what I measure.
bret

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