Fig. 89.
I now introduce between the prisms B and n a rectangle, s s′, of plate glass, 6 feet long, 2 inches wide, and one-third of an inch thick, which is to be thrown into longitudinal vibration. The beam from L passes through the glass at a point near its centre, which is held in a vise, c, so that when a wet cloth is passed over one of the halves, c s′, of the strip, the centre will be a node. During its longitudinal vibration the glass near the centre is, as already explained, alternately strained and compressed; and this successive strain and pressure so changes the condition of the light as to enable it to pass through the second prism. The screen is now dark; but on passing the wetted cloth briskly over the glass a brilliant disk of light, three feet in diameter, flashes out upon the screen. The vibration quickly subsides, and the luminous disk as quickly disappears, to be, however, revived at will by the passage of the wetted cloth along the glass.
The light of this disk appears to be continuous, but it is really intermittent, for it is only when the glass is under strain or pressure that the light can get through. In passing from strain to pressure, and from pressure to strain, the glass is for a moment in its natural state, which, if it continued, would leave the screen dark. But the impressions of brightness, due to the strains and pressures, remain far longer upon the retina than is necessary to abolish the intervals of darkness; hence the screen appears illuminated by a continuous light. When the glass rectangle is shifted so as to cause the beam of polarized light to pass through it close to its end, s, the longitudinal vibrations of the glass have no effect whatever upon the polarized beam.
Thus, by means of this subtile investigator, we demonstrate that, while the centre of the glass, where the vibration is nil, is subjected to quick alternations of strain and pressure, the ends of the rectangle, where the vibration is a maximum, suffer neither.[44]
§ 7. Vibrations of Rods of Wood: Determination of Relative Velocities in Different Woods
Rods of wood and metal also yield musical tones when they vibrate longitudinally. Here, however, the rubber employed is not a wet cloth, but a piece of leather covered with powdered resin. The resined fingers also elicit the music of the rods. The modes of vibration here are those already indicated, the pitch, however, varying with the velocity of the sonorous pulse in the respective substances. When two rods of the same length, the one of deal, the other of Spanish mahogany, are sounded together, the pitch of the one is much lower than that of the other. Why? Simply because the sonorous pulses pass more slowly through the mahogany than through the deal. Can we find the relative velocity of sound through both? With the greatest ease. We have only to carefully shorten the mahogany rod till it yields the same note as the deal one. The notes, rendered approximate by the first trials, are now identical. Through this rod of mahogany 4 feet long, and through this rod of deal 6 feet long, the sound-pulse passes in the same time, and these numbers express the relative velocities of sound through the two substances.
Modes of investigation, which could only be hinted at in our earlier lectures, are now falling naturally into our hands. When in the first lecture the velocity of sound in air was spoken of, many possible methods of determining this velocity must have occurred to your minds, because here we have miles of space to operate upon. Its velocity through wood or metal, where such distances are out of the question, is determined in the simple manner just indicated. From the notes which they emit when suitably prepared, we may infer with certainty the relative velocities of sound through different solid substances; and determining the ratio of the velocity in any one of them to its velocity in air, we are able to draw up a table of absolute velocities. But how is air to be introduced into the series? We shall soon be able to answer this question, approaching it, however, through a number of phenomena with which, at first sight, it appears to have no connection.