6. One person takes 112 steps a minute and another 116. How many times a minute will the two walkers be in step? How many times a minute will one be advancing the left foot just when the other advances the right?
7. Why is it necessary to have a standard pitch?
8. How can the pitch of the sounds given by a phonograph be lowered?
9. How many beats per second will occur when two tuning forks having frequencies of 512 and 515 respectively, are sounded together?
10. Which wires of a piano give the highest pitch? Why?
(6) Tone Quality, Vibrating Air Columns, Plates
345. Quality.—The reason for the differences in tone quality between notes of the same pitch and intensity as produced, e.g., by a violin and a piano, was long a matter of conjecture. Helmholtz, a German physicist (see p. 397) first definitely proved that tone quality is due to the various overtones present along with the fundamental and their relative intensities. If a tuning fork is first set vibrating by drawing a bow across it and then by striking it with a hard object, a difference in the quality of the tones produced is noticeable. It is thus evident that the manner of setting a body in vibration affects the overtones produced and thus the quality. Piano strings are struck by felt hammers at a point about one-seventh of the length of the string from one end. This point has been selected by experiment, it having been found to yield the best combination of overtones as shown by the quality of the tone resulting.
Fig. 337.—Chladni's plate.
