Y USING Chladni's method, it is possible to show the nodal lines on any plate from the position taken up by the sand when the plate is in vibration. The plate is clamped at one point and a violin-bow drawn across the edge. In this method it is difficult to produce high notes on the plate or to reproduce any desired figure at will. With some type of vacuum tube it is easy to make a loud steady note and to apply this note to the plate for an indefinite time. The first method which suggests itself is to sound a note on a tuning fork or pipe before a microphone. The resulting electric current is then run through an amplifier. The output of the power amplifier actuates some type of loudspeaker. The best type for this particular purpose is an electrodynamic loudspeaker with a corrugated aluminum diaphragm. To the center of this diaphragm is soldered a three-inch copper rod which has a conical cap. The Chladni plate has a small hole at its center which fits over the cap, supporting and balancing the plate. It is also possible to clamp the plate at any point and apply the vibrating rod to its under side. The same apparatus may be used for membranes except that the membrane can never be balanced upon the cone, but must be held in both hands by its frame and pressed against the vibrating member. Experiment shows, however, that a musical note sounded before a microphone is likely to vary in pitch and so destroy any sand figure which is forming. The best source of a sustained note is a suitable triode valve. When this valve is placed in the proper circuit, it will produce electrical vibrations varying from several a second to many -thousands. When these vibrations pass through a power amplifier and into the loudspeaker, they will set the cone into violent vibration and also produce a musical note. • The membranes used in these experiments are ten inches in diameter or ten inches square. They are made of paper glued on to a wooden frame.
Membranes of this size will not form sand figuresColwell, Phil. Mag. 12, 320 (1931). 228 for high notes because the tension becomes irregular. The sand lines shown in Fig. 1 are for notes lower than five hundred cycles per second.The brass Chladni plates, if sufficiently thin, will vibrate at much higher frequencies, but another difficulty arises in getting loudspeakers which will vibrate at such frequencies since they are made so as to have the greatest efficiency below five thousand per second. For frequencies above ten thousand per second, a maghetostricrive rod will be found satisfactory. A pure nickel rod inserted in an inductance coil displaces the loudspeaker of the previous set-up. Such a rod will vibrate with a high amplitude at frequencies up to fifty kilocycles a second. The higher the vibrations, the more complicated the figures become, but finally a point is reached at which the plate cannot follow the vibrations of the rod; this is at approximately fifteen kilocycles per second. The sand lines of Fig. 2 were produced with the nickel rod vibrating between twelve and fifteen ki...
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