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(b) Does the presence or absence of the sound-board have any effect on the length of time the string will continue to vibrate ?
Ant. (a) See pp. 86 and 87.
(b) Yes; the string if connected with a sound-board does not vibrate so long as it would if it were not so connected.
4.  (a) When a closed organ pipe is blown too strongly the note goes up a twelfth. In the case of an open pipe, it goes up an octave. Give the reason for this.
(J) Calculate the approximate vibration number of a closed organ pipe 2 ft. long, assuming the velocity of sound to be 1,100 ft. per sec. An*.—See pp. 107, 108, and 102. Approximate vibration number == ^p; = 137*5
5.  (a) Why is the interval beween two notes estimated by the ratio of the vibration numbers and not by their difference ?
(b) What are the vibration ratios of a fifth, a major third, and an equal temperament semitone.
Am. (a) Because the ratio of the vibration numbers for any par­ticular interval is constant; while the vibration numbers themselves vary with the pitch, and therefore their difference would vary.
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6.    Explain the production of the scale on the slide trombone. Am.—See p. 114.
7.    Why are the various notes of a flute or clarinet put out of tune with each other when the joints of the instrument are pulled out so as flatten the pitch as much as possible.
Am.—The fundamental note of such an instrument is that due to the whole length from mouth-piece to the other end. The other notes are due to the distance between the mouth-piece and the apertures corresponding to these notes. Now these distances are at certain ratios to the whole length. If the joints be lengthened all these ratios are changed, and therefore the intervals are not the same as before.
8.  (a) Investigate by Helmholtz's method the relative consonance of a fourth and a major third.
(b) Why does the ear recognize want of correct intonation in the case of the octave more easily than in the case of the major third ?
Am. (a) Seep. 191.
(b) In the octave, powerful beats are found between loud first and second partials. In the major third much fainter beats between weaker fourth and fifth partials, see pp. 176 and 180.