At 12:36 PM -0600 1/31/02, Ron Nossaman wrote: RH >>There is no need to posit any kind of physical, substantial motion >>to account for the bouncing of the fork. In fact, such an idea is >>thoroughly erroneous. The reflection from the end of the fork >>causes the stress wave which is, in fact, what we are talking about >>here, to demonstrate itself as a kind o displacement of the end. >>This is strain and does not require the fork to be moving to occur. >>Such an idea is at odds with every analysis of this subject. > >And which analyses are these? Where might I find every one of these >analyses of the details of handle movement in a tuning fork ruling out mass >reaction?................. I'd like to know where you get _your_ notion of bodily movement of the shank of the fork, what brand of "geometry and mathematics" leads you to your conclusions and how Newton has misled you. Here is what two eminent acousticians in direct descent from Newton have to say on the question: "A tuning fork can be considered to be two vibrating bars, both clamped at their lower ends" [Morse IV. 15] Here is Rayleigh's rationale of the tuning fork: "[With one clamped bar] in consequence of the oscillation of the centre of inertia, there is a constant tendency towards the communication of motion to the supports, to resist which adequately the latter must be very firm and massive. In order to obviate this inconvenience two precisely similar springs and loads may be mounted on the same framework in a symmetrical manner. If the two loads perform vibrations of equal amplitude in such a manner that the motions are always opposite...the centre of inertia of the whole system remains at rest and there is no tendency to set the framework into vibration. ... In fact any part of the motion which does not conform to the condition of leaving the centre of inertia unmoved is soon extinguished by damping." [Theory of Sound I.56] From this immobile centre of inertia will radiate periodic compressions of the particles. If the shank of the fork is held loose, a small amount of this energy will be transmitted into the fluid of the fingers but most of it will be reflected internally. Particles all round the surface of the shank will be "dancing" in and out with minuscule amplitude of oscillation but with great force, so that unless the fork is held firmly in contact with the resonant system (e.g. the table) the momentum of these molecules will be sufficient to push the whole fork away. This is not because the fork is moving up and down (or sideways) but because the particles at the surface are oscillating. It makes very little difference to the amplitude of the transmitted sound whether you press the fork vertically against the table or flank-wise parallel to the table. JD
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