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Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)
As the speed of rotation approaches the object's natural frequency, the object begins to resonate, which dramatically increases system vibration. The resulting resonance occurs regardless of orientation. When the rotational speed is equal to the natural frequency, then that speed is referred to as a critical speed.
[4] When the source of the sound wave is moving towards the observer, each successive cycle of the wave is emitted from a position closer to the observer than the previous cycle. [4] [5] Hence, from the observer's perspective, the time between cycles is reduced, meaning the frequency is increased. Conversely, if the source of the sound wave is ...
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
Collision frequency describes the rate of collisions between two atomic or molecular species in a given volume, per unit time. In an ideal gas , assuming that the species behave like hard spheres, the collision frequency between entities of species A and species B is: [ 1 ]
The phase velocity c p (blue) and group velocity c g (red) as a function of water depth h for surface gravity waves of constant frequency, according to Airy wave theory. Quantities have been made dimensionless using the gravitational acceleration g and period T , with the deep-water wavelength given by L 0 = gT 2 /(2π) and the deep-water phase ...
The value of the magnitude of an object's four-velocity, i.e. the quantity obtained by applying the metric tensor g to the four-velocity U, that is ‖ U ‖ 2 = U ⋅ U = g μν U ν U μ, is always equal to ±c 2, where c is the speed of light.
Frequency dispersion in groups of gravity waves on the surface of deep water. The red square moves with the phase velocity, and the green circles propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red square overtakes two green circles when moving from the left to the right of the figure.