Physics

by Willis E. Tower; Thomas D. Cope; Charles H. Smith; Charles M. Turton

If the end of the wire spring shown in Fig. 317 is struck the first few turns of the spring will be compressed. Since the spring possesses elasticity, the turns will move forward a little and compress those ahead, these will press the next in turn and so on. Thus a compression wave will move to the end of the spring, where it will be reflected and return. Consider the turns of the spring as they move toward the end. On account of their inertia they will continue moving until they have separated from each other more than at first, before returning to their usual position. This condition of a greater separation of the turns of the spring than usual is called a rarefaction. It moves along the spring following the wave of compression. The condensation and rarefaction are considered as together forming a complete wave. Since the turns of wire move back and forth in a direction parallel to that in which the wave is traveling, these waves are called longitudinal.

Fig. 318.—Longitudinal waves (1) in a spring, (2) in air, and (3) graphic representation showing wave length, condensations, and rarefactions.

324. The transmission of a sound by the air may be understood by comparing it with the process by which a wave is transmitted by a wire spring. Consider a light spring (Fig. 318, 1) attached at the end of a vibrating tuning fork, K, and also to a diaphragm, D. Each vibration of the fork will first compress and then separate the coils of the spring. These impulses will be transmitted by the spring as described in Art. 315, and cause the diaphragm to vibrate at the same rate as the tuning fork. The diaphragm will then give out a sound similar to that of the tuning fork. Suppose that the spring is replaced by air, and the diaphragm, by the ear of a person, E, (Fig. 318, 2.) when the prong of the fork moves toward the ear it starts a compression and when it moves back a rarefaction. The fork continues vibrating and these impulses move onward like those in the spring at a speed of about 1120 ft. in a second. They strike the diaphragm of the ear causing it to move back and forth or to vibrate at the same rate as the tuning fork, just as in the case of the diaphragm attached to the spring.

325. Graphic Representation of Sound waves.—It is frequently desirable to represent sound waves graphically. The usual method is to use a curve like that in (Fig. 318, 3). This curve is considered as representing a train of waves moving in the same direction as those in Fig. 318 1 and 2, and also having the same length. The part of the wave A-B represents a condensation of the sound wave and the part B-C represents a rarefaction. A complete wave consisting of a condensation and a rarefaction is represented by that portion of the curve A-C. The portion of the curve B-D also represents a full wave length as the latter is defined as the distance between two corresponding parts of the adjacent waves. The curve, Fig. (318, 3) represents not only the wave length, but also the height of the wave or the amount of movement of the particles along the wave. This is called the amplitude and is indicated by the distance A-b. Since the loudness or intensity of a sound is found to depend upon the amount of movement of the particles along the wave, the amplitude of the curve is used to indicate the loudness of the sound represented. All of the characteristics of a sound wave may be graphically represented by curves. Such curves will be used frequently as an aid in explaining the phenomena of wave motion both in sound and in light.

326. Reflections of Sound.—It is found that a wave moving along a wire spring is reflected when it reaches the end and returns along the spring. Similarly a sound wave in air is reflected upon striking the surface of a body. If the wave strikes perpendicularly it returns along the line from which it comes, if, however, it strikes at some other angle it does not return along the same line, but as in other cases of reflected motion, the direction of the reflected wave is described by the Law of Reflected Motion as follows: The angle of reflection is always equal to the angle of incidence. This law is illustrated in Fig. 319. Suppose that a series of waves coming from a source of sound move from H to O. After striking the surface IJ the waves are reflected and move toward L along the line OL. Let PO be perpendicular to the surface IJ at O. Then HOP is the angle of incidence and LOP is the angle of reflection. By the law of reflected motion these angles are equal. In an ordinary room when a person speaks the sound waves reflected from the smooth walls reinforce the sound waves moving directly to the hearers. It is for this reason that it is usually easier to speak in at room than in the open air. Other illustrations of the reinforcement of sound by reflection are often seen. Thus an ear trumpet (Fig. 320), uses the principle of reflection and concentration of sound. So-called sounding boards are sometimes placed back of speakers in large halls to reflect sound waves to the audience.

Fig. 319.—Law of reflection.
Fig. 320.—An ear trumpet.

327. Echoes.—An echo is the repetition of a sound caused by its reflection from some distant surface such as that of a building, cliff, clouds, trees, etc. The interval of time between the production of a sound and the perception of its echo is the time that the sound takes to travel from its source to the reflecting body and back to the listener. Experiments have shown that the sensation of a sound persists about one-tenth of a second. Since the velocity of sound at 20°C. is about 1130 ft. per second, during one-tenth of a second the sound wave will travel some 113 ft. If the reflecting surface is about 56 ft. distant a short sound will be followed immediately by its echo as it is heard one-tenth of a second after the original sound. The reflected sound tends to strengthen the original one if the reflecting surface is less than 56 ft. away. If the distance of the reflecting surface is much more than 56 ft. however, the reflected sound does not blend with the original one but forms a distinct echo. The echoes in large halls especially those with large smooth walls may very seriously affect the clear perception of the sound. Such rooms are said to have poor acoustic properties. Furniture, drapery, and carpets help to deaden the echo because of diffused reflection. The Mormon Tabernacle at Salt Lake City, Utah, is a fine example of a building in which the reflecting surfaces of the walls and ceiling are of such shape and material that its acoustic properties are remarkable, a pin dropped at one end being plainly heard at the other end about 200 ft. away.