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54 PITCH AND RAPIDITY OF VIBRATION. [II. § 26.
as the distance from the origin of sound increases is a direct consequence of the connexion between loudness and extent of vibration. We have seen [§ 22] that the further an air-particle is from the point where a sound is produced, the smaller will be the extent of the vibration into which it is thrown by the sonorous wave. Hence, as the sound advances it will necessarily become feebler, provided always that the waves are permitted to spread out in all directions. If they are confined, say, in a tube, the intensity of the sound will for considerable distances remain practically constant. We have here the theory of the message-pipes which are used in large establishments to enable a conversation to be carried on between distant parts of a building. A whisper, inaudible to a person close to the speaker, may by their means be perfectly well heard by a listener at the other end of the tube.
26. We have next to enquire to what mechanical causes differences in the pitch of musical sounds are to be referred. Rough observation at once indicates the direction in which we must look. If we draw the point of a pencil along a rough surface, first slowly and then more quickly, the sound heard will be distinctly shriller the more rapid the movement of the pencil. As its point passes over the minute elevations and depressions which constitute