2. A steel rod (such as the prong of a long tuning-fork) is free to vibrate at one end and is fixed at the other. Where will the nodes be situated in the first and in the second of its higher partial nodes of vibration, and what will be approximately the relative pitches of those higher tones compared with the fundamental P
Ans.—For 1st overtone the node will be about a fourth or a fifth of its length from the free end. For 2nd overtone the one node will be nearer than this to the free end, while the other will bisect the length between this node and the fixed end. The relative pitches of the fundamental, and 1st and 2nd overtones will be approximately as
4 : 25 : 70.
3. Many organists will tell you that when the room where the organ is gets hot, the reeds in the trumpet stop and other reed-pipes "get flat" in tone. Is this allegation true? Explain the facts that have originated this idea.
Am.—Eeeds do slightly flatten with rise of temperature (see p. Ill), but the other pipes of the organ, the flue-pipes, sharpen much more rapidly with increase of temperature, so that the reeds seem to flatten by contrast.
4. Describe a method of analysing a complex tone and of discovering its constituent tones.
Ans.— See pp. 69, 70, 71.
5. Violinists in order to produce the effect of tremolo upon an open string resort to the following method: The open string alone is bowed whilst a tremolo fingering is performed upon the next higher string at the point corresponding to the octave above the note of the open string. Give physical explanations to account for the effect being the same as though the tremolo had been executed on the bowed string.
Ans.—The open string when bowed vibrates not only as a whole but also in halves, producing the upper octave; this sets the string above vibrating by resonace and as this is subjected to the tremolo fingering, a tremolo effect is produced, and this in its turn reacts upon the open string.
6. (a) Why are dampers always provided in a pianoforte ? (b) What is the evidence for the existence of damping in the mechanism of the ear.
Ans.—(a) Dampers are provided : (1) to silence a string after it has been struck, and (2) to prevent other strings sounding by resonance.
(b) The shake in music (say 10 tones to a second) can be clearly heard throughout the greater part of the musical scale, but as we get very low in pitch, they sound bad and rough, and their tones begin to mix. This is not due to the instrument producing the tones, for they are so on all instruments. It is consequently due to the ear, that is the damping in the ear is not so rapid and complete for the lower tones as for those above.