HANDBOOK OF ACOUSTICS - online book

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

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300                    HAND-BOOK OF ACOUSTICS.
6.    Why does a stopped pipe give a hollow sound compared with the sound of an open pipe ?
Am — See pp. 106, 107.
7.    "Why does a major seventh sound more dissonant than a major second.
Am.—Because in the first case the higher tone beats at a semitone distance with the second partial of the lower, while in the second case the beating distance is about twice that interval.
8.    Why should students of music study the elements of Acoustics ? Am.—Briefly, because the laws of Acoustics are the foundations of
music; for example, a knowledge of acoustics is necessary in order to understand the construction of the scale ; the estimation of intervals ; the fundamental facts of harmony; the nature and origin of dissonance, temperaments, &c.
Miscellaneous Questions.
1. Find the approximate length of the C C4 pipe on the open diapason 8 ft. What ia the pitch of note on open diapason 8 ft. length, the pipe of which is 1 ft. 6 ins. ?
Am.—To find approximate length of 0 C$ pipe, C C being 8 ft, it is first necessary to assess the interval between the two. This is a chromatic semitone. The vibration fraction for this interval being |A (see p. 51) the 8 ft. length of the C C pipe must be divided by 25 and multiplied by 24—
8 X 24 -J- 25 = 7i|- = 7 ft. 8 ins. approximately.
To find out the pitch of a pipe of 1 ft. 6 ins. in length. In the first place it must be some note between the 2 ft. and 1 ft. C, viz., between
I
-------"— Now 2 ft. X 3 ft. = 6 ft., and 6 ft. -f- 4 ft. =
1 ft. 6 in., and as ^ is the vibration ratio of a Fourth, the required pitch is F.
2. (a) How does a string vibrate as a whole, and at the same time in segments, to form harmonics? (b) How is the tone of the (one segmental) fundamental kept up, although the harmonics are sounding? (c) Does the fundamental vibrate first, then the segments for the 8ves, 5ths, 4ths, &c, one after the other respectively, or do they all vibrate together ? (rf) What causes the harmonics; i.e., what causes the string to assume the different segments, seeing it only gets plucked to vibrate its own (one segmental) fundamental ?
Am.(a) Students often have a difficulty in realising that a body can have several independent motions at the same time, yet the phenomenon is a very common one. Take the case of two persons in the opposite corners of a carriage of an express train, tossing a ball