Sound An Elementary Text book for Schools And Colleges

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The frequencies of the fundamentals of rods of the same thickness and material but different lengths are inversely proportional to the squares of the lengths.
Rods of the same length and of rectangular section, the direction of vibration being parallel to one of the sides of the rectangle, have frequencies proportional to the length of the side of the rectangle in the plane of vibration, and independent of the dimensions of the rectangle at right angles to the direction of vibration. The latter
... relation is easily seen to be true, for if a rod is doubled in width in the direction at right angles to the plane of vibration, both the inertia and the elastic forces are doubled, and therefore the period is unaltered.
If the thickness in the plane of vibration is doubled, the inertia is doubled but the elastic forces are increased eightfold, and therefore the period is halved.
220. Wheatstone's Kaleidophone. It will be seen then that a rod of rectangular section fixed at one end has different periods of vibration in two directions at right angles 186 RODS, PLATES AND BELLS [CH.


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