EXAMINATION PAPERS. 297
Am.—Let x represent the weight required.
Then V n = $ or J7j = 4 therefore x = 22£ kilos.
6. An open organ pipe being 20 ft. long, find the wave-lengths, and the vibration numbers of its fundamental note and its first two overtones (v = 1100 ft. per second).
Ans.—Wave-lengths are 40, 20, 13J ft.
Vibration numbers are 27i, 55, 82J ft. See pp. 39 and 99.
7. What are the Diatonic and the Chromatic Semitones, and their vibration numbers ?
Ant.—See pp. 48 and 49.
8. A note of 226 vibrations per second and another of 340 are sounded together, each being accompanied by its first two over-tones. Show that two of the over-tones will give two beats per second.
Am.—Second over-tone of the first = 226 X 3 = 678. First over-tone of the second = 340 X 2 = 680.
Difference = 2.
Royal University of Ireland, 1898.
1. Describe a sound wave iu air. Am.—See pp. 16, 17, and 18.
2. How may the pitch of a musical note be found by experiment. Am.—See pp. 31, 32 ; 35, 36, 37, or 151 and 152.
3. A stretched string gives the note doh. How must its tension be altered so that the note emitted may be sol ?
Am.—The tension must be increased 2\ times. See p. 87.
4. Describe the condition of the air in an open organ-pipe when mounding its first overtone.
Am.—See p. 105 with fig. 54 (B).
5. Why do sounds travel faster in water than in air?
Am.—Because the elasticity of water in proportion to its density is greater than the elasticity of air in proportion to the density of air. See p. 20.
6. Give some account of the physical basis of harmony. See Chapter XVI.
7. What interval added to a Major third will make an Octave?
5 8 2 Ans.—A Minor Sixth : for j X g = T
See Chapter V.
8. Describe Helmholtz's Double Siren. Am.—See p. 34 with fig. 22.