The Pendulum Method traces the curve. Demonstration
المؤلف:
GEORGE A. HOADLEY
المصدر:
ESSENTIALS OF PHYSICS
الجزء والصفحة:
p-229
2025-11-23
15
On the opposite sides of a baseboard, about 40 cm. square, fasten two uprights 102 cm. long above the upper surface of the base. Fix a crosspiece to the top of these. Bore a hole in the middle of this and fit a handle so that it will turn snugly. Make a lead disk 10 cm. in diameter and 2 cm. thick, and through the middle drill a hole 5 mm. in diameter. Suspend this by three cords as in Fig. 1,
and at the point A tie these three cords to two others which run through the holes B and C in the crosspiece and then through a hole in the handle H. Wind a ring of copper wire R about the two cords, so that it can be slipped up or down, and unite the two into one, as RA. Place a glass plate on the baseboard, and sift sand upon it from a tin flour dredge. Select a glass rod or tube that will slip easily. through the hole in the disk, and make one end small and rounded in a Bunsen flame. Put the rod through the disk; then draw the disk back and release it so that it will vibrate across the base in the direction DE. The disk swings as a pendulum from the points C and B, and the rod traces a straight line in the sand. Vibrate again in a direction GF, at right angles to DE. The rod will again trace a straight line, swinging from the point R. Now draw the disk aside midway between these directions, and when it is released, the rod will trace a curve which will be the result of combining the two motions, and the form of which will depend upon the relative lengths of the two pendulums, i.e. of the points K and R from the middle of the lead disk.
The distance of K from the middle of the disk can be kept at 1 m. by turning the handle H; and by making the distance of R from the middle of the disk such that the short pendulum vibrates three times while the long one vibrates twice, the curve corresponding to the combination of the tones sol and do is obtained. If the times of vibration are as 2: 1, the curve will represent the combination of a tone and its octave. By applying the law of the pendulum for length and time of vibration, the length of the short pendulum can be easily found for most musical intervals.
Figure 2 shows some of the simpler figures that can be obtained if the ratios of vibrations are such as 1:2, 2:3, 3:4.
If the ratios are of large numbers, the figures become more complicated.
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