A complete view of Acoustical Science & its bearings on music, for musicians & music students.

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from one to the other. The ball has several independent motions. While it is being tossed across the carriage, it is also travelling in the direction in which the train is moving, and at the same speed as the train. Moreover, the ball and the train are both moving from west to east at the rate of several hundred miles an hour, a motion due to the earth's rotation. Lastly, the ball, train, and earth are whirling round the sun at a still more rapid rate. Thus, the ball has four distinct motions at the same time. In the same manner, there is no real difficulty in conceiving a stretched string vibrating as a whole, and at the same time in two or more segments, (b) The string vibrating as a whole gives the fundamental, and vibrating in two, three, four, or more segments at the same time, produces also the first, second, third, fourth, and higher harmonics, or as it is better to term them, overtones, (e) All together, (d) Stretch a heavy cord ten or twelve feet long between two fixed points; the heavier it is the more slowly it will vibrate, and thus its vibration will be the more easily seen. An india-rubber tube filled with sand answers the purpose very well. Set it vibrating by a gentle movement near the centre; it will vibrate as a whole, i.e., with one vibrating segment. Bring it to rest and now strike it somewhat sharply at about \ of its length from one end. It will then vibrate in two segments. By following up this line of experiment, it may be made to vibrate in three or more segments, the number being only limited by the flexibility of the cord. Moreover, when the tube is set vibrating, say at |th its length from the end, it is not difficult after a few trials to get it to vibrate in halves and as a whole at the same time. Now, a stretched string producing a musical tone vibrates in exactly the same way, but owing to its lightness and flexibility, it is found impossible to get it to vibrate as a whole, that is, in one segment alone; some other segmental vibration is always present under ordinary musical conditions.
3.    A vibrating tuning-fork is held over a tall cylinder, into which water is gradually poured. Describe and explain the variation that takes place in the sound of the fork. How could you employ this apparatus to find the velocity of sound, the period of the vibration of the fork being given ?
Ans.—For first part of question, see pp. 61 and 62. For second part, Hold vibrating fork over cylinder; gradually pour in water until the air column in cylinder gives out its maximum resonance. Then measure distance from surface of water to mouth of cylinder. Multiply four times this distance by the vibration number of the fork and the product will be the distance sound travels per second; i.e., the velocity of sound.
4.    What name is given to the difference between a diatonic and a chromatic semitone ?