Dipole Effects and Leaks in Soundboard; was Isolated Air-Movement

Lesher, Trent J. tlesher@sachnoff.com
Sat, 31 Jan 2004 18:35:12 -0600


Hi Terry, 

I noticed this question when you posted it a few days ago and thought I might be able to shed some light on part of it.    

You wrote:

"We all know the acoustic effects of placing a hi-fi speaker on a large panel 
or on the panel of a sealed box compared to holding the speaker out in mid 
air - especially mid-range and bass speakers. What about holes for nose 
bolts through the soundboard and the limited distance from the top of the 
soundboard on a grand, around the outside of the outer rim, to the underside 
of the soundboard. Surely the two soundboard surfaces are not totally 
isolated from one another. Perhaps the distance around the rim is large 
enough that soundwaves do not interfere with one another. Perhaps the holes 
in the panels are not large enough for a significant amount of air to pass 
and cancel out soundwaves. But perhaps there is sound degradation from one 
or both of these sources. Any insight into this? " 

Years ago, I was involved in loudspeaker design -- driver and crossover circuit design through enclosure design.  All the factors and relationships have gone kind of fuzzy on me, but what I remember is that holes in a baffle can function as friction losses, reactively as tuned mass/spring systems, and/or simply holes making an acoustical short-circuit, the kind of effect you are wondering about.  Since there is no air-spring factor involved in a soundboard (like there is in a sealed or ported box), the hole in a soundboard couldn't be a tuned (i.e. tuned-resonance) mass reactance, but, depending on the size of the hole and the thickness of the soundboard, it could still function reactively and act analogously to an inductor in an electrical circuit, and the losses would flow most freely the lower the frequency, but subject to the limitations of resistance (friction).  It will probably be a combination, varying with frequency -- for instance, once the wavelength of the frequency involved is small compared to the size or depth of the hole, the rules change.  Also, when it's functioning with reactive components, the "filtering" of the hole has not just amplitude effects, but also time-domain effects, so there will be frequency-dependent phase rotations that affect the degree of wave cancellation.  The positions of the holes make a difference too.   

I think the effect would not be great in this situation for the frequencies involved, but I'd like to know for sure myself.  If you want to give me some rough board dimensions, hole sizes (include the diameters of bolts going through), the distances of any boundaries (like a plate or brace or post) that are nearer to the panel than the diameter of the hole, and locations, I'll try to refresh my brain on all this and answer relative to a specific piano that you know, otherwise I'll just use the 30 y.o. M&H Model 50 upright I have here.  (Yeah, yeah, I know all too well, lots of problems with that vintage.  Later on I may be bugging you guys for advice whether/how to improve it.) 

As for the wave cancellation path taking the long way around, I believe the sound pressure level from a perspective measured directly in "front" of either side of the panel (and at a distance, say more than 1 meter, at which near-field effects aren't so great) should be down about -3db at the frequency which has a quarter wavelength equal to the path length from center to center of the opposing surfaces, and will fall off rapidly (at -18dB/oct?) below that.  The shortest relatively free path gives the worst-case scenario.  Taking out my handy sewing tape measure, I get a shortest path of 54" for the M&H 50.  I'm assuming the top lid doesn't present much of an obstacle whether it's open or closed.  So that would be  that would be about 63Hz based on speed of sound in air of 13,560 inches per second.  As was discussed somewhere on this list earlier, -3dB, half-power, isn't subjectively nearly as drastic as it sounds; it's actually near the lower limit of a difference in level that most people will notice, though more attuned ears can notice fractions of that.  Unlike pitch sensitivity, which is very fine, amplitude sensitivity is on a very compressed scale, owing to the extremely wide range in the amplitude of sounds on earth, which is why either a 10-watt stereo system or a 300-watt stereo system are both of a reasonable human scale for the same living room.

Anyway, if I remember something I read (in the 5 lectures?) correctly, even if you measure directly off the soundboard with a contact pickup (thus taking acoustic radiation efficiency out of the equation for the moment), most pianos have very little energy below about 70 Hz anyway, certainly not this one.  So from that at least it seems like 63 Hz (just below the second partial of C#1) is more than a respectable bottom end response.

But it's more complicated than this, so the above is pretty far from a complete answer.  If the Model 50 were round so all paths were the same, we should expect maybe some major boominess or chestiness centering around the half wavelength of the path length, at about 126 Hz (centering between the fundamentals of B2 and C3) and serious cancellation centering on the full wavelength, two octaves above, between B3 and C4.  Though it wouldn't be precisely focussed around 126Hz, there probably is some congestion or boominess in the tenor from this, especially when you're sitting at the piano and the back is close to a wall.  But the various longer path lengths also count, and they improve the picture by extending the response further down, and also by spreading the effects throughout a range of frequency centers, reducing, but not necessarily eliminating, strong peaks and valleys.  

(There definitely was such a boomy-chesty congestion in this piano, which I had attributed -- maybe at least partially incorrectly I think now -- to low soundboard impedance.  It did improve a lot -- with a lot of trial & error, and without making the tone so terrible in other ways like I was expecting -- when I wedged a hardwood block in behind the low end of the long bridge and a post and another somewhere between the high end of the bass bridge and the bottom part of the liner.)    

But also, theoretically there is a total null in acoustic output if you center yourself edgewise to the panel.  Most pianists don't play in that position (but with a grand, they're not really "in front" of one side or the other either) but a seated listener could easily be close to such a position.  A total null -- complete cancellation -- assumes complete symmetricality orthogonal to the plane of the panel, in both the panel itself and the environment.  So in reality from this edgewise listening perspective, the casework would have pretty major effects in the midrange, and, speaking of a grand now, the floor boundary would have uneven effects in the bass -- the round-trip path from the SB to floor and back would reinforce the fundamentals around Bb3, if you were pretty close to the piano, but might cause a fundamental attenuation centering around Bb2 or so -- but then the dissipation could benefit total output from other perspectives because now the radiation from the top of the soundboard wouldn't get as much unwanted destructive or constructive interference in those frequencies.  But of course the reinforcement would reinforce whatever back-wave interference effects there were, sort of squirting pressure waves out the sides of the standing waves.  Energy-wise, standing wave reinforcement doesn't come for free, but almost, because the internal impedances of the piano are so much greater than any air-impedances.  (It might be coincidence, but that actually corresponds pretty well with the fact that my upright sounds less muddled and more open about 2 or 3 feet from the wall.) 

I never worked with panel speakers -- electrostatics and ribbons -- which seem like they would probably be the best loudspeaker model for a soundboard, much less have I performed measurements on a piano, so I personally don't have the experience to have a sense for what all this means for overall sound.  A buddy of mine had a pair of "giant" Soundlabs (7feet tall, 36 inches wide) that seemed to give solid response down to 35Hz (from a normal listening position).  They were also curved across the front (cylindrically curved as a matter of fact!), with a maximum concavity of 5" or so in the back.  In the case of these and other panel speakers, response does depend on things like distance from the back wall, and Soundlab may have designed in a rising bass response in the actual panel movement to compensate for cancellation, but still, at those dimensions I wouldn't expect to be able get much of anything solid at 35 Hz, but these seemed to. 

Some people add "wings" to the their panel speakers, and this does substantially extend and fortify low frequency response from the listening position, and I presume it would do something similar for a piano.  But a question is, how much mechanical energy at the relevant frequencies is even there in the soundboard in the first place?  It won't make much difference to boost up acoustic efficiency at 40Hz if there's nothing much to boost up.  But it seems like total soundpower output -- as opposed to SPLs from any one particular perspective -- from a piano would be reduced substantially -- from frequencies one or two octaves higher (than 40Hz) and on down -- by these back-wave or dipolar effects, so though it may turn out to be a desirable effect overall, it's certainly not a negligible issue at all.

Although there would be total null in terms of pressure changes directly edgewise to a panel perfectly symmetrical orhogonal to its plane, but, close to the edge at least, air would be rushing back and forth between the front and back. It's the opposite of a standing wave, where there's little movement, but lots of pressure variation.  (The existence of movement within a null explains how even with an ideally symmetric panel situation with a complete edge-wise null, energy can be transmitted through the null to go on to act as acoustic energy interfering both constructively and destructively with the front wave.)  This might be a good case of a little knowledge leading to inanity, but I've heard of "velocity-sensitive" (as opposed to "pressure-sensitive") microphones.  I wonder what such a microphone makes out of oscillating air molecules in the absence of pressure variations? Are our ears only pressure sensitive for hearing tones? 

Open baffle and panel speakers and store a lot less energy than sealed box or ported speakers, which is often an advantage dear to the musically oriented.  More subtle definition and texture.  So whatever the drawbacks, pianos have that going for them.  (Now as far as using a big piece of wood as a diaphragm and all the unique combination energy storage and lossiness involved in that, well, I guess that's just a piano.) 

This is making me realize how much I have yet to understand about yet another topic.  I keep having so many experiences where because of incomplete models or wrong assumptions, things worked either much better or much worse than they were "supposed" to.  Then you poke around and figure out some factors you missed and go deeper, and hopefully come up with a better model for next time, and then somewhere down the line you find out that that one's not working too well for a certain situation and the cycle continues.  With all the boundary conditions, irregular casework, mechanical transmission through the floor, etc., with a piano, there might be some surprising results if you took measurements from a variety of pianos under different conditions.  It seems like there's probably already a lot better info out there, maybe one of the academic researchers doing work on piano acoustics, or maybe Del Fandrich or Ron Overs or someone can point us in the right direction.  

As for the holes, although there's no substitute for somebody taking frequency spectrum measurements from a variety of positions and then plugging the holes up and doing it again, I think I can handle that question a little more satisfactorily than the other one.  I wish I still had the equipment to take some measurements myself, but various upheavals took their toll some years ago.  But give me some data if you want and I'll see what I come up with. 

Best r egards,

Trent Lesher

(tuning student, amateur pianist)

 

Terry Farrell wrote: 

"Ron O. wrote: "...the primary purpose of the panel is to prevent air leaking past the 
ribs." 

We all know the acoustic effects of placing a hi-fi speaker on a large panel 
or on the panel of a sealed box compared to holding the speaker out in mid 
air - especially mid-range and bass speakers. What about holes for nose 
bolts through the soundboard and the limited distance from the top of the 
soundboard on a grand, around the outside of the outer rim, to the underside 
of the soundboard. Surely the two soundboard surfaces are not totally 
isolated from one another. Perhaps the distance around the rim is large 
enough that soundwaves do not interfere with one another. Perhaps the holes 
in the panels are not large enough for a significant amount of air to pass 
and cancel out soundwaves. But perhaps there is sound degradation from one 
or both of these sources. Any insight into this? 

Terry Farrell" 

----- Original Message ----- 
From: "Overs Pianos" <sec@overspianos.com.au> 
To: "Pianotech" <pianotech@ptg.org> 
Sent: Thursday, January 29, 2004 9:16 AM 
Subject: Re: Rib Thinning 


> Richard, 
> 
> >Do I understand you to say that dowels even just through the panel 
> >and bridge are not all that great an idea ? ... or just through the 
> >ribs ? 
> 
> Dowelling into ribs is the big no no, but it is more critical as 
> Terry Farrell mentioned, when the ribs are designed entirely to 
> support the down bearing. It doesn't matter at all to dowel through 
> the panel, particularly with a rib crowned board where the primary 
> purpose of the panel is to prevent air leaking past the ribs. It is 
> quite common for manufacturers to dowel the bridges to the panel, but 
> again it is not a great idea to use large dowels. While the bridge 
> mass helps to produce sustain in an instrument, its stiffness helps 
> to spread the support of the rib set evenly across the panel. 
> 
> There is so much development waiting to be done with sound boards. 
> Its a very interesting area and I'm looking forward to some of the 
> projects we are undertaking this year. 
> 
> By the way folks, we've got an Australasian convention coming up in 
> the South Australian capital city of Adelaide this July. We've got a 
> couple of visiting experts, Ron Nossaman and Roger Jolly, presenting 
> classes. For further online details on the South Australian 
> convention, please visit; 
> 
> http://aptta.org.au/sa_conv_news.html <http://aptta.org.au/sa_conv_news.html>  
> 
> Best, 
> Ron O. 
> -- 
> OVERS PIANOS - SYDNEY 
>     Grand Piano Manufacturers 
> _______________________ 
> 
> Web http://overspianos.com.au <http://overspianos.com.au>  
> mailto:info@overspianos.com.au <mailto:info@overspianos.com.au>  
> _______________________ 
> _______________________________________________ 
> pianotech list info: https://www.moypiano.com/resources/#archives <https://www.moypiano.com/resources/#archives>  
> 

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