CONTENTS.

CHAPTER XII.

§§ 255—266 . . . . . . . . . . 49
Vibrations in tubes. General form for simple harmonic motion original: "simple harmonic type". Nodes points in a standing wave where there is no motion and loops points of maximum motion, now commonly called antinodes. Conditions for an open end of a tube. In standing waves original: "stationary vibrations", there must be nodes at intervals of 1/2 $λ$ $λ$ is the standard symbol for wavelength. Reflection of pulses at closed and open ends. Problems in compound vibrations. Vibration in a tube caused by external sources. Cases where both ends are open. Progressive waves waves that move through a medium rather than staying in place caused by disturbances at the open end. Motion originating within the tube itself. Forced vibration of a piston. Kundt's experiments a method for measuring the speed of sound using dust patterns in a glass tube. Summary of results. Vibrations of the column of air in an organ pipe. The relationship between wavelength and pipe length. Overtones higher frequency sounds produced alongside the fundamental pitch. The frequency of an organ pipe depends upon the type of gas used. Comparison of the speed of sound in various gases. Examination of vibrating air columns using membranes and sand. Examination by König's flames a device using gas flames to visualize sound waves. Curved pipes and branched pipes. Conditions to be met at the junctions of connected pipes. Pipes with variable cross-sections original: "variable section". Approximate calculation of pitch for pipes with variable cross-sections. The influence of changing cross-sections on progressive waves. Variation of density.

CHAPTER XIII.

§§ 267—272 a . . . . . . . . . . 69
Aerial vibrations in a rectangular chamber. Cubical boxes. Resonance of rooms the way sound reflects and builds up in an enclosed space. Rectangular tubes. The combination original: "composition" of two equal wave trains. Reflection by a rigid, flat wall. [Nodes and loops.] George Green’s investigation of the reflection and refraction of plane waves at a flat surface. The law of sines also known as Snell's Law, describing how waves change direction when passing between materials. The case of air and water. Cases where both substances are gases. Fresnel's expression mathematical formulas for the behavior of light or sound at an interface. Reflection at the boundary of air and hydrogen. Reflection from warm air. Tyndall's experiments John Tyndall's studies on how sound is affected by atmospheric conditions like fog and heat. Total internal reflection. Reflection from a plate of a specific thickness. [Reflection from a corrugated surface. Cases where the second substance is impenetrable.]

CHAPTER XIV.

§§ 273—295 . . . . . . . . . . 97
Random initial disturbances in an unlimited atmosphere. Poisson's solution a mathematical formula used to predict wave propagation in three dimensions. Verification of the solution. Limited initial disturbances. The case of two dimensions. Deducing a solution for a disturbance that is continually renewed. Sources of sound. Simple harmonic motion original: "harmonic type". Verification of the solution. Sources distributed over a surface. An infinite flat wall. A sheet of double sources. Waves in three dimensions that are symmetrical around a central point. Simple harmonic motion. A wave of compression or rarefaction cannot exist by itself. Continuity through the origin original: "pole". Initial circumstances. The velocity potential of a given source. Calculation of the energy emitted. The speaking trumpet an early megaphone designed to direct and amplify the voice. The theory of conical tubes. The position of nodes. The combination of vibrations from two simple sources of the same pitch. Interference of sounds from electrically powered tuning forks. Points of silence. The existence...