Sot's]) SKxsaTtos. It would he expected that there should be some connection between the nature of the vibrations of the vibrating body, that of the waves produced, and that of the sound heard. Such is the ease. A noise is al ways produced by an irregular, disconnected dis turbance in the air; and this in turn is due to an irregular succession of vibrations, each last ing for a brief interval. A simple musical note is always clue to a simple harmonic train of waves, and this to a simple harmonic vibration. The loudness of the note varies directly with the amplitude of the waves; whatever increases the amplitude of the waves increases the loudness of the sound, and vice versa. It is increased, there fore, by an increased amplitude of the vibration; and it decreases as the distance front the ear to the vibrating body is increased. (It should not be thought, however, that numerical values can be given the loudness of a sound, or that there is any fixed numerical relation between the am plitude of the waves and the intensity of the sensation.) The pitch of the note depends upon the wave-number of the waves entering the ear; whatever increases the wave-number "raises" the pitch, and rice rersd. Therefore, if the ear and the vibrating body are at a fixed distance apart, and at rest with reference to their positions in space, the pitch will vary directly with the fre quency of the vibrating body: thus we often use the expression, "a pitch of 21)0," meaning the pitch of a sound produced by a vibrating body which makes :300 complete vibrations in one sec ond. If, however, the vibrating body is ap proaching the ear, or if the ear is approaching the vibrating body, the number of waves enter ing the ear is greater than it would be if there were no such motion; and so the wave-number is greater than the frequency of the vibrating body, and the pitch of the sound is raised. Sim
ilarly, if the distance between the ear and the vibrating body is increasing, the wave-niunher is less than the frequency of the vibration, and the pitch is lowered. This change of pitch, due to the relative motions of the ear and the vibrat ing body in the surrounding medium, is known as Doppler's Principle (q.v.), and is illustrated by the sudden drop in pitch if one stands on the platform of a railway station and listens to the whistle of a locomotive passing at a high speed.
.1 complex musical note is always duo to a complex train of waves, and this, in turn, to a complex vibration, if there is, only one vibrating body. Further, two notes which differ in qual ity may be shown to he duo to complex trains of waves which differ in complexity. But it should be noted that all experimental evident:e points to the idea that differences in relative phases of the component trains of waves do not cause differences in time quality of the sound heard. In other words, two complex trains of waves made up of the stone simple waves will produce the same sound, regardless of the phases in the two trains. This may be explained by saying that the ear automatically resolves a complex train of waves into its simple harmonic component trains. hears the simple tones due to each of these, and, therefore, has a eoniplex sen sation. This statement is called "Ohm's law for sound-sensation."