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INTENSITY OF MUSICAL SOUNDS.                53
black. Move the glass slip slowly along under the tuning-fork. The latter, as it vibrates, will remove the lamp-black, and leave a clean wedge-shaped trace on the glass, as seen in fig. 29. As the width of the trace at any point is evidently the amplitude of the vibration of the fork, at the time that point was below it, we see that the amplitude of the vibrations of the fork gradually decreases till the fork comes to rest; and as the sound decreases gradually till the fork becomes silent, we see that the intensity of its sound depends upon the amplitude of its vibrations.
It is obvious, that the greater the amplitude of the vibrations of a sounding body, the greater will be the amplitude of the vibrations of the air particles in its neighbourhood; thus we may conclude, that the intensity of a sound depends upon the amplitude of vibra­tion of the air particles in the sound wave. But it is a matter of common experience, that a sound becomes fainter and fainter, the farther we depart from its origin ; therefore, we must limit the above statement thus: the intensity of a given sound, as perceived by our ears, depends upon the amplitude of those air particles of its sound wave, which are in the immediate neighbourhood of our ears. This leads us to the question: " At what rate does the in­tensity of a sound diminish, as we recede from its origin ? " We may ascertain the answer to this question, by proceeding as in the analogous case of heat or light. Thus, let A, fig. 30 be the origin of a given sound. At centre A, and with radii of say 1 yd., 2 yds., 3 yds., describe three imaginary spheres, B, C, D. Now, looking on sound, for the moment, as a quantity, it is evident that the quan­tity of sound which passes through the surface of the sphere B is identical with the quantity that passes through the surface of the spheres C and D. But the surfaces of spheres vary as the squares of their radii; therefore, as the radii of the spheres B, C, and D are 1, 2, and 3 yds. respectively, their surfaces are as l2 : 2* : 38, that is, the spherical surface C is four times as great, and D 9 times as great, as the spherical surface B. We see, therefore, that the quantity of sound, which passes through the surface of B, is, as it were, spread out fourfold as it passes through 0, and ninefold as it passes through D. It follows, therefore, that one square inch of C will only receive £ as much sound as a square inch of B, and one square inch of D only £ as much. Thus, at distances of 1, 2, 3, from a sounding body, the intensities are as 1, |, and £ ; that is, as we recede from a sounding body, the intensity diminishes in pro­portion to the square of our distance from the body, or more con-