On Thu, Feb 17, 2011 at 2:34 PM, Mark Schecter <mark at schecterpiano.com> wrote:
> Hi, Nick.
>
> Thanks for presenting this definition, I appreciate it, and I think it is
> generally helpful. But I would like to raise some questions about it,
> You say: "... thus in a broad but accurate sense the piano string’s
> uncoupled and feeble attempt to excite large zones of air demonstrates a
> very low amplitude."
>
> That [the string's] ability to excite much
> vibration in air is small, is true. But coupling it to the soundboard does
> not raise the energy level/amplitude of the signal.
Mark, not to pick on you, but It is right here where you have fallen
into the typical trap of confusing the precise meanings of the terms
energy and amplitude; these cannot be equated. You are in good company
with untold thousands of engineering and physics college students. You
are correct in that string coupling does not raise the energy level,
but wrong in thinking that coupling also does NOT raise the amplitude
of the output signal. String coupling DOES raise the amplitude hence
the acoustical power output. I included a link in my paper to
http://www.indiana.edu/~emusic/acoustics/amplitude.htm
and at that link you can read that "Both amplitude and intensity are
related to sound's power" and "amplitude is measured in the amount of
force applied over an area." Note that amplitude is related to energy
but is not the same thing at all. The presence of amplitude always
implies oscillation and power of some magnitude, and that energy is
being used to do some form of work. Energy is simply available for
tapping into, like the electric outlets in your house. If we can
assume your power outlets as a starting point then no work is being
done until you turn on the coffee maker. Later you can turn on your
bandsaw. The power and amplitude issues are dramatically different,
but the same power is available for both workhorses.
Now power (aka amplitude) is defined as work per time. That is, if you
can run a mile in 3 minutes and your plumber takes 5 minutes, then you
have demonstrated more power than your plumber since have you squeezed
more "work" and effort into covering the mile in less time. Simple
math shows, if we arbitrarily assign a factor of 100 for the work
required, that your power output is 100/3 = 33 and the plumber's is
100/5 = 20. Energy is not even in the equation yet is always implied.
Now we're getting somewhere.
I took it axiomatically to be understood that a highly-tensioned but
uncoupled string, activated by an energy impulse of a given quantity
will continue its vibratory action for a relatively long period of
time. This vibratory action is called mechanical energy. Let's say the
vibratory lifetime is three minutes. Now in these three minutes, due
to internal friction of the wire and gravity, the string's mechanical
energy naturally damps down exponentially over time and attains
equilibrium. But during its long vibratory life it is unable to move
much air due to its tiny surface area. Now since it is given that we
want sound to impact our ears, I stated that the string's attempt at
moving air, that is in converting mechanical energy to acoustical
energy, was feeble.
Now in this little model of a vibrating string, the string acts as a
transducer in that it is converting mechanical energy into acoustical
energy, although doing it poorly for our needs. These are simply
different forms of our chameleon friend, energy. Yes, both exhibit
oscillatory and harmonic motion, but a vibrating string exhibits
mechanical energy and vibrating air exhibits acoustical energy. This
must simply be accepted as true and there can be no opinion on this. A
piano payed in a vacuum will not convert the mechanical energy of the
string/soundboard in to acoustical energy.
Now moving on. By coupling this same string, at the same tension and
carrying an identical energy impulse, to a large and thin mass
assembly called a soundboard we have given the vibrating string a very
strong companion to help out with the work load. The two companions
will now get the work done faster as the string and board are now
considered to be one oscillating member (for sake of brevity). The
much larger surface area of the board is now able to activate large
zones of air. The acoustical power (amplitude) is increased
dramatically, but at a serious cost to sustain or longevity of output
as was had by the uncoupled string acting alone. In acting to enlarge
the power it also acts proportionally as a brake on the system.
So the trade off is this. We know that energy is conserved --- energy
in equals energy out in both the uncoupled and coupled systems. The
difference is that the coupled system accomplishes more work by
dissipating the energy input in a shorter time period. And where there
is more work per time we have more power. The three minute sustain of
the uncoupled string has now been reduced to, say, 30 seconds. Nothing
has been lost, nothing has been gained as to energy, but the
acoustical power (amplitude) has been dramatically increased. A small
signal has been made large, hence amplified, but its life time has
been proportionally shortened. Regarding energy transduction, the
soundboard is a device called a transducer; as regarding work and
acoustical power output, the soundboard is an amplifier.
You get all this when you say,
>What such coupling does
> do is propagate the vibration to many more air molecules than the string
> can, due to the soundboard's much larger surface area.
But partially miss the point by confusing conservation of energy with
modification of power output when you say,
>But the energy was
> never feeble at all, in fact it was always entirely sufficient to the task.
> ... But the basic form of energy, mechanical
> vibration, has not changed - only the material or medium through which it is
> propagating has changed. (Or so I would assert - is any of this wrong?)
I hope that what I wrote above clarifies the confusion I see here.
>
> Later you say: "Any device that converts one form of energy, say
> vibrational, to another form of energy, say sound, is a transduction device
> or transducer."
>
> I think this statement obscures the fact that sound already IS vibrational
> energy, and therefore there is no transduction needed.
Not exactly, and we must be precise. Sound is acoustical energy.
Vibrational energy is a murky term. It would have been better had I
used the specific term mechanical energy as I have consistently tried
to use in this reply. I will go back and change "vibrational energy"
in the quoted passage to "mechanical energy". Nonetheless, everything
around us is vibrating and in oscillation. In order for our
discussions to be meaningful we must be specific about what form that
vibrational energy takes or transduces into.
>The only difference
> between vibrating string and vibrating air is in the material that is
> vibrating, metal to wood to air to eardrum. What IS needed is efficient
> propagation of that vibrational energy, from the source (string) through the
> bridge and soundboard into the medium (air) which the soundboard provides.
Any use of the term efficiency per this subject matter must carefully
understood in a relative way. It may surprise you that efficiency is
not only NOT happening, but is neither required nor sought. Impedance
mismatching (inefficiency) of the string to the soundboard assembly IS
required or no standing waves will ensue, hence no sustain. Efficiency
implies an immediate power dump of string vibrations via the board. We
would get a very loud power burst accompanied by a virtual infinite
amplitude spike, like a tuned snare drum, but no sustain at all.
Impedance is a related subset of this discussion, but a large subject
in its own right. I will be teaching on this via PowerPoint, physical
gadgets and created audio files at the upcoming WESTPAC convention in
San Fransisco. There are practical implications to us as techs, and to
be basically grounded in this subject is as much about practical
matters as theory. Hope to see some of you there.
> Of course, the soundboard is temporarily the medium as well, but only as a
> link in the mechanical chain from vibrating string to vibrating air to
> vibrating eardrum. Thus there is no transduction or change ...
Transduction and change do occur. Again, the use of the terms
vibrating string, vibrating air and vibrating eardrum are too vague
and general. Transduction means a change in form of these various
energies. Better to say the changes take place thus: the mechanical
energy of the string changes to acoustical energy of sound, and then
back to mechanical energy in the eardrum. The ear-system, then, acting
as a transducer takes the impulses and converts them into tiny
electrical signals for the brain to sort out. Transduction and
transducers --- everywhere you look. In order to fully grasp this we
need to distance ourselves from grouping everything into "vibrational
energy" soup. This is a foggy term when we require clarity.
>
> Later yet you say: "We can say that the job of piano sound amplification is
> to take the weak vibrational signal of the uncoupled string (low amplitude)
> and “boost” it via coupling in order to generate a powerful signal (high
> amplitude). It doesn’t matter that additional energy is not present for this
> to happen."
>
> Again, I would say that this mis-characterization as "weak" actually
> confuses the issue, as the vibrational signal is inherently as strong as it
> needs to be to cause its ultimate intended result, sound. It is only "weak"
> in its ability to move air, due to its small surface. When we connect it to
> a large surface, voila', without adding energy, we create sound (vibrations
> in air) of much larger (apparent) amplitude.
In disagreeing with me you have essentially agreed with me. But you
are again confusing the conservation of energy with its effect of
work-energy output. These are cause and effect domains. If you object
to the term weak then ignore it. Its intended use was to equate weak
with the string's inability to transduce its mechanical energy into
useful acoustical power-amplitude. You are correct in implying here
that original energy input "is inherently as strong as it needs to be
to cause its ultimate intended result, sound."
> You go on: "Still, an analog to electrical amplification exists in that a
> ppp blow to a key can be barley audible; now add more energy with a fff blow
> and we have increased amplitude, hence more amplification with the attendant
> volume and power."
>
> Here, I feel that the analogy to electrical amplification is also confusing
> as presented, because amplification takes the SAME signal and makes it
> larger, whereas your example contrasts a smaller original signal with a
> larger original. This is not analogous, as it happens at the source, not the
> broadcast end of the chain.
You are correct as far as you state things RE signal boosting. But the
idea was, if we turn up the volume on our guitar amps, we get more
acoustical power (increased amplitude) in direct proportion to the
enhanced electronic circuitry gain. The amplified circuitry is only a
means to an end, that end being enhanced acoustical power. The only
way to "turn up the volume" on an acoustic piano is to play it harder,
hence more volume, sustain and higher amps. Both knob turning in one
case, and more finger force in the other are the means to the end of
increasing amplitude. In addition, my aim was to show (partly through
implication) that amplification in electronic EQ does not always mean
sound amplification or reinforcement. It often means that circuits and
electronic systems are often amplified ("gained up or down") that
have no function related to sound propagation.
But as to electronically produced amplification, speaker cones are too
massive to be shaken by tiny electrical impulses and must by "gained
up" (amplified) to much larger pulses, those strong enough to rattle
the speaker cone. So, in order for a guitar amp to create larger
acoustical power, a dedicated circuit must exist to amplify small
signals into larger ones. And specifically this is all that electronic
amplification means. The analogy was to show that gains up or down in
the piano can only take place by altering the force of the blow, i.e.,
by adding more energy to the system. Again, if this is of little help
to you, throw it out.
>
> I do agree that it's perfectly acceptable to call the soundboard an
> amplifier for purposes of explaining to lay customers what it does.
Well, then I've accomplished my primary goal. I suggest you reread my
paper, include what was added here, take what is useful to you and
dump the rest. Thanks for your input and questions. I will reread my
paper and make a change or two for consistency.
I think I am done with this topic for now. If I have I brutally
misstated something please let me know; otherwise I'll leave it to
you, Mark, and others to bat around.
>
Thanks, and all the best!
>
Nick
>
>
> On 2/17/11 10:05 AM, Nicholas Gravagne wrote:
>>
>> ENERGY TRANSDUCTION VS SIGNAL AMPLIFICATION
>> ,,, a simple statement by
>> Nick Gravagne
>> Thursday, February 17, 2011
>
--
Nick Gravagne, RPT
AST Mechanical Engineering
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