Graphical Method of Combining Vibrations
المؤلف:
GEORGE A. HOADLEY
المصدر:
ESSENTIALS OF PHYSICS
الجزء والصفحة:
p-228
2025-11-23
52
It is frequently desirable to represent graphically the relation that exists between the vibrations of tones of different pitches. The method usually adopted is to consider the vibrations of the two bodies to be made at right angles with each other, and to construct a curve that shall be the result of the two vibrations combined. If the vibrations producing the tones c and f are to be combined, the curve can be made graphically as follows:
Suppose a point moving back and forth along AC, in simple harmonic motion corresponding to uniform motion around circle H, to represent the vibrations that produce c, and suppose a point moving along AB in simple harmonic motion with reference to circle D to represent the vibrations that produce f (Fig. 1). Since the ratio of the numbers of vibrations in these two tones is 1: 4/3, the body sounding the tone f vibrates eight times while the body sounding e vibrates six times, and therefore makes one sixth of a vibration while the body sounding c makes one eighth of a vibration. Lay off the circumference DEF into six equal parts, and the other circumference into eight. From the points of division draw lines perpendicular, respectively, to AB and AC, and prolong them; then their intersections will give the points for the required curve. In order that the curve connecting the points shall be smooth, intermediate points must be determined.
The curve representing the combination of any other two tones can be constructed in the same way.
الاكثر قراءة في الميكانيك
اخر الاخبار
اخبار العتبة العباسية المقدسة
