Vibratory Motion and SoundGinn, Heath, 1882 - Broj stranica: 135 |
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acceleration amplitude antinode approximately arithmetical mean auxiliary circle beats called centre CHAPTER COMPOSITION compound constant crank curve denote described diagonal difference of phase displacement distance double ellipse elliptic harmonic motion epoch equal equation extreme positions fixed force fork give HARMONOGRAPH Hence Hooke's law horizontal interval length longitudinal maximum mean position mean value middle point musical nodes number of vibrations obtained opposite directions pantagraph parallel parallelogram particle pendulum period of vibration perpendicular pipe pitch plane produce projection prongs pulleys pulse quarter period radii radius ratio rectangle resultant revolving right angles round S.H. motions sides simple harmonic motion simple harmonic vibration simple tones slot sonorous undulations sound statical energy stationary undulation straight line string tangent tion tube uniform circular motions velocity of propagation vertical vibrations per second vibratory motion vt-x waves travelling y=a cos
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Stranica 107 - ... continues to vary uniformly with the rate denoted by dy at the given point, the value of-— will become constant. The generatrix will now continue to move uniformly in the direction of the curve at the( given point, and therefore the value which -~ has at this point is that of the trigonometrical tangent of the inclination of the curve to the axis of x at this point. The line now described by the generatrix is called a tangent line to the...
Stranica 36 - Now we have shown above that a positive value of the functional determinant <pu\f/v — <pv^u means that Z2 is on the positive side of Zi, so that in this case Z moves in the positive sense (that is, in the direction from the positive axis of x to the positive axis of y) with increasing values of a. With a negative value Z moves in the opposite direction. Let us now suppose that the curves x = const. and y — const. in the uv plane intersect except on a certain curve where their direcu FIG.
Stranica 40 - LENGTH, is the distance from any particle, to the next particle that is in a similar position in its path, and is moving in the same direction.
Stranica 91 - Since the velocity of propagation of a wave through any medium varies directly as the square root of the coefficient of elasticity and inversely as the square root of the density...
Stranica 91 - ... in one direction and then in the opposite, a series of compressions and extensions are produced in alternate succession. But each compressed portion tends to relieve itself by expanding into the neighbouring air, which is thus in its turn compressed, and the extended portions in like manner tend to communicate extension.
Stranica 60 - ... the equation of a parabola, whose vertex is at a distance b from the central point of the vibrations, and focus at the distance ^ from the vertex.
Stranica 60 - Of the other curves, the most interesting is the symmetrical figure of 8 which corresponds to 8 = — and 8= — — , the path being the same for both these cases, but traced in opposite directions.
Stranica 19 - B (Fig. 10) revolve round the same circle with equal and opposite angular velocities, they will meet at both ends of one fixed diameter.
Stranica 102 - ... a reversed pulse, which travels along the string from this end to the other, where it is again reflected and reversed.