No branch of classical physics is older in its origins yet more modern in its applications than acoustics. The sensation of pitch is a psycho-physiological matter and is only imperfectly understood. Helmholtz, that Leonardo da Vinci of modern times, wrote his monumental work, the Sensations of Tone, largely from the physiological approach. The first is the rise of a whole new industry, devoted to the realistic reproduction of speech and music through the mediums of the radio and the phonograph. Synopsis No branch of classical physics is older in its origins yet more modern in its applications than acoustics. In addition, the centimeter, the gram, the dyne, etc. In the strict sense, the word sound should be used only in connection with effects directly perceivable by the human ear.
¹ The restrictions that the function be single-valued and continuous are easily met in the case of the vibrations of material bodies, and the theorem is therefore of the greatest use in acoustics. The second, less beneficent in nature, arose as the result of war needs, both in the field of undersea signaling and in connection with problems in aeronautics. The student is cautioned not to use the word loudness as synonymous with intensity. But it is very helpful to students to gain an understanding of mechanical waves before trying to comprehend the more subtle and abstract electromagnetic ones. Subsequent topics include longitudinal waves in different gases and waves in liquids and solids; stationary waves and vibrating sources, as demonstrated by musical instruments; reflection and absorption of sound waves; speech and hearing; sound measurements and experimental acoustics; reproduction of sound; and miscellaneous applied acoustics. Waves in Three Dimensions 4. Nevertheless, a consideration of particle vibration theory is basic to the understanding, of the more complicated motions of extended bodies such as strings, bars, plates, etc.
The phenomenon of beats, in sound, is a familiar one. Fundamental Particle Vibration Theory 2. In the realm of pure physics the use of high frequency longitudinal waves has become a valuable means for the study of interatomic forces in solids, both at normal temperatures and near the temperature of absolute zero. Longitudinal Waves in Different Gases. There is an interesting distinction between what might be called mathematical and audible beats. This is a fact of fundamental practical importance in the production of music. The general scope of the war work in connection with underwater signaling is well known.
We are using loudness here in the purely qualitative sense. Thoughtful comparison between acoustics and other branches of physics and engineering has brought to light little realized interrelations, of great use to all fields concerned. With ordinary sound intensities a real difference frequency is never observed, that is, a third musical note is never evident. Late in the nineteenth and during the early twentieth century, finishing touches to the already elegant formulation of the mechanics of sound propagation were added by Rayleigh and Lamb, whose writings on the subject have become standard treatises. Music has long felt itself an art to be insulated as far as possible from the mechanics of science. To obtain a typical coefficient, An, for the sine series, both sides of Eq. The simplest case to consider is when the frequencies are the same.
Since and since the integration will always be over an integral number of cycles, the result of all integrations on the right-hand side of Eq. The audible effect of beats contains none of the subtleties discussed above. There is even evidence that it is during the transient period of attack, for instance, that a violin is recognized as such, rather than as, say, a cello. Interest in acoustics has stimulated further study along physiological lines. Laymen of all kinds are interested in speech and song, music and noise. All three equations can also be obtained by considering the projection, on a diameter of a circle, of the motion of a particle moving around the circle with a constant speed, as is usually shown in elementary physics.
Therefore no recurring beat phenomenon, in the strict mathematical sense, will exist. Other applications of acoustics will be considered in Chapter 12. The electrical circuit analogs discussed in Chapter 5 are a good example of this. In the nineteenth century, the results of the experiments of Doppler, Kundt, Kelvin, and others added to the growing body of the subject. Fundamental particle vibration theory -- 2.
As we shall see in Chapter 9, the relation between frequency and pitch is a complicated one. At the receiving end, whether it be at the ear or at a microphone, amplitudes may be unbelievably small. First, there is the precise, absolute calibration of the equipment over a wide range of sound frequencies and intensities. Subsequent topics include longitudinal waves in different gases and waves in liquids and solids; stationary waves and vibrating sources, as demonstrated by musical instruments; reflection and absorption of sound waves; speech and hearing; sound measurements and experimental acoustics; reproduction of sound; and miscellaneous applied acoustics. Waves in Liquids and Solids7. I-10 The use of electrical analogs. Whenever this approximation may not be made, the vibrating surface may be broken up into smaller areas, infinitesimal if desired, the sum effect of which is equivalent to that of the total surface area of the actual source.
Since those early experiments, much quantitative work has added to the knowledge. As so often occurs when interest in a subject revives, other fields, like those of medicine and pure physics, have been stimulated to make use of new tools and new refinements of the older theoretical work. Reflection and absorption of sound waves -- 9. From the discussion just concluded, a mixture of frequencies not bearing a whole number relation is equivalent to no repetitive steady state vibration. When it is realized that not only the string properties but also the shape and complex characteristics of the body of the instrument greatly determine the nature of the radiated sound, one is ready to accept the fact that the design of a high quality musical instrument is as much a matter of art as of science. In addition, if the whole number relation does second, when they have executed 203 and 202 cycles respectively, they will be in phase again.
Musicians are closer to science than they perhaps realize when they play musical instruments and wonder as to the quality of the sound flowing from them. The velocity and displacement bear a 90° relationship, while acceleration and displacement are 180° apart. When the two vectors are in the positions shown in Fig. These are, it would appear, permanent interests which will probably persist, even with the competing glamour of the atom and its nucleus! However, since the two amplitude vectors are rotating with nearly the same angular velocity, it is clear that at whatever angle to the x-axis coincidence occurs, the two vectors will have only slight relative displacement by the time they do reach the horizontal, and the above statements are, for all practical purposes, valid. This is because the ear is sensitive only to the envelope of the sum function, as in Fig.