Page:Elementary Text-book of Physics (Anthony, 1897).djvu/187

§ 148] act as a reed, and the player may at will produce many of the different overtones. In that way melodies may be played without the use of keys or other devices for changing the length of the air-column.

Vibrations may be excited in a tube by placing a gas flame at the proper point in it. The flame thus employed is called a singing flame. The organ of frhe voice is a kind of reed pipe in which little folds of membrane, called vocal chords, serve as reeds which can be tuned to different pitches by muscular effort, and the cavity of the mouth and larynx serves as a pipe in which the mass of air may also be changed at will, in form and volume.

146. Longitudinal Vibrations of Rods.— A rod free at both ends vibrates as the column of air in an open tube. Any displacement produced at one end is transmitted with the velocity of sound in the material to the other end, is there reflected without change of sign, and returns to the starting-point to be reflected again exactly as in the open tube. The fundamental tone corresponds to a stationary wave having a node at the centre of the rod.

147. Longitudinal Vibrations of Cords.— Cords fixed at both ends may be made to vibrate by rubbing them lengthwise. Here reflection with change of sign takes place at both ends, which brings the wave as it leaves the starting-point the second time to the same phase as when it first left it, and there must be, therefore, as in the open tube, 1, 2, 3, 4, etc., vibrations while the wave travels twice the length of the cord. The velocity of transmission of a longitudinal displacement in a wire depends upon the elasticity and density of the material only. The velocity and the rate of vibration are, therefore, nearly independent of the stretching force.

148. Transverse Vibrations of Cords.—If a transverse vibration be given to a point upon a wire fastened at both ends, everything relating to the reflection of the wave motion and the formation of stationary waves is the same as for longitudinal displacements. The velocity of transmission, and consequently the frequency of the vibrations, are, however, very different. They depend on the stretching force or tension and on the mass of the cord per unit