>Hmmmm.... Agreeing that the total about of energy obviously does not >increase that must mean that all other things being equal, a freely open >vibrating string (no soundboard) would have much longer sustain, right? I >imagine the soundboard to be "condensing" the energy, releasing it in a >shorter, louder span; >"That which burns twice as bright burns half as long" >-k Surely that is correct. Surely the coupling of the string to the soundnboard produces an acoustical transformer? Think of the string at rest. No movement (setting aside tiny air currents in the room, or whatever). When you strike a key and that causes the hammer to strike the string, you have input some energy into the system. All of that energy has come from you. At the point when the hammer hits the string, your "inputting" is already over and done, because let-off means that you are not in contact with the hammer; it's travelling on its own the last few millimtres to the string, under the momentum your energy input imparted. Having struck the key, you can now stand away from the piano. Your role as energy supplier is finished. What happens within the system into which you imparted energy, depends on how the system is configured. But there will be no more energy coming into the system after you have stuck the key (assuming you don't strike it again!) How the system MANAGES that energy which you have just input, depends on the system. Imagine a single domino standing upright on the ground. You flick it with a certain force, and it falls over. It hits the ground with a certain "snap" or vibration, which is dissipated in the ground and the air (partly as sound). Now imagine you stand the domino in front of another and another and another, etc, all within touching distance. You strike the domino with *exactly the same force* as before. In falling over, it hits and knocks over its neighbour, which does the same, etc etc. Your intial blow, can cause thousands, maybe millions, of dominos, to fall over. Yet your energy input is the same in both cases. It's how that energy is deployed within the system, because of how the sytem in configured, that makes the difference. The uncoupled piano string with a certain amount of energy imparted to it, will sound for a certain length of time, displacing a certain amount of surrounding air in the process. If you couple the string such that it is forced to set in motion a large spruce board, which displaces a much greater quantity of air, the movement of the string will not continue as long. It cannot, for no extra energy is available, yet you are forcing it to move a greater load. The work is harder; therfore with a given amount of energy, it must continue for a shorter time. I suppose another way to look at it is to imagine a gallon bucket with a hole in it, filled with water. You can only ever get a gallon of water out of that bucket (from one filling). You can get it out slowly, through a tiny hole, or quickly, through a large hole, but it will only ever be a gallon, since that's all that can be put in. Best regards, David Boyce
This PTG archive page provided courtesy of Moy Piano Service, LLC