At 7:05 AM +0000 1/25/02, Phillip L Ford wrote: >What I was asking is whether the point that the accelerometer is >attached to has to be moving for the accelerometer to have a reading? If >the accelerometer is attached to the top of the bridge and the accelerometer >is showing a reading then that point at the top of the bridge must be moving, >regardless of what is happening to the molecules underneath it in the bridge >or soundboard. If that point was sitting fixed in space with the molecules >beneath it doing whatever they are doing then the accelerometer would show >no reading. Do you agree with this? That would depend on the type of accelerometer used and its g rating and frequency range. There are all sorts and some would tell you nothing useful at all. Besides, we have been dealing with the vibration initiated at the string termination in isolation and considering it in a plane normal to the soundboard. There will also be transverse modal vibrations of the soundboard/bridge affecting the whole system and superimposed on the vibrations due to the flexure of the strings. Owing to various factors the actual angle of the strings' flexures will be unpredictable and need to be factored in from separate measurements using who knows what devices. In practice I'd say the whole test would be quite a challenge for any experienced lab technician. I'm no expert in the use of accelerometers. I've recently obtained two of them but have not yet devised experiments for putting them to use and am not sure how I'm going to set about it or whether the two units I've been supplied with are going to answer the questions I want the answers to. We don't need any fancy devices or any doctorates of philosophy to investigate the phenomenon in question. Here's a simple experiment anyone can carry out at no cost and which will provide evidence direct to the eye and ear. RUBBER BRIDGE EXPERIMENT ________________________ On my string-making machine I stretch a No.23 wire (or a covered string) at a tension of about 80 lb. The speaking length will be about 120 cm. and the frequency about 100 c/s, but anything will do. About 120 cm from the end I set up my bridge/soundboard between the string and the machine bed. Soundboard No. 1 is a whetstone and soundboard No. 2 is a cigar box. My bridge is two rectangular india-rubber erasers one on top of each other (effectively one thickness) about 25 mm. high. When I pluck the string, its transverse vibrations are clear to see and if my eyes were better, I'm sure I'd see movement at the string termination too. Needless to say with soundboard No. 1 I hear very little sound. Now I take my accelerometer, which is a straightish length of 2 mm. copper wire with a wooden bead at one end and a point at the other. (I also went out and bought a mechanic's stethoscope following Robin's suggestion, but this was actually less effective because of its stiffness and mass. The copper wire, slightly bent, can follow the vibrations without damping them significantly) Now I set the string vibrating and it sustains pretty well because the amount of energy being lost is not great. I now hold the point of the wire to the rubber right next to the string termination and listen with the bead held against the little flap in front of the ear-hole, whose name I don't know. The movement at the string termination is clearly felt as a vibration in the wire and the sound of the string is clearly heard complete with some quite high harmonics. I then place the point of the wire on the whetstone directly below the string termination, and you'll not be surprised to hear I hear next to nothing. Since the whetstone is rigid and immovable, no vibration is taking place. I next move the point of the wire to positions on the rubber bridge further and further down from the string termination and as I do so, the amplitude of the sound diminishes and the higher partials disappear. If I take soundings along the top of the bridge, the further I get from the string termination, the less vibration I get, not surprisingly. Next I replace the whetstone with the cigar-box soundboard. Now, of course I can hear the sound of the string radiating from the cigar-box. I take the same aural measurements as before, and the vibrations at the termination are indistinguishable from those I heard when the soundboard was made of stone; but as I take soundings downwards through the bridge the amplitude falls off less steeply and the sound is not extinguished where the bridge meets the soundboard. However, I have lost quite a few upper harmonics. These have been absorbed in the bridge, or damped, or "filtered out". Indeed I have come across several references where the bridge is referred to as a mixer and a filter. So the radiated sound that I hear contains the fundamental and a part of the harmonic spectrum, but not everything that was fed in at the top. So, does the bridge move? One thing I have surely to allow is that every particle between the string termination and the soundboard has moved before the soundboard is disturbed, and several more in the immediate vicinity, but each of them has moved a different amount and perhaps in different directions. The more massive or the stiffer the soundboard, the less the particles near the bottom of the bridge will move in comparison with those near the top. So long as there is some flexibility in the soundboard, every particle between it and the string end will move. If anyone likes to regard this as bodily movement, they are free to do so, but I don't. It is a localized disturbance of particles that tends to compress and to bend and this disturbance travels where it can and bounces back where it can't. It's effect is to compress and to bend to varying degrees. I have my flame-thrower ready for anyone that needs to inform me that piano bridges are not made of india-rubber, but I'll be happy to hear any serious criticisms of this experiment. JD
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