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PhiJ
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In the wave equation, what is u, is it the amplitude?
If it is, how can it be a vector?
If it is, how can it be a vector?
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YESPhiJ said:In the wave equation, what is u, is it the amplitude?
Why couldn't it be ?If it is, how can it be a vector?
A phasor is just a rotating vector (angle : wt), expressed in a XY-plane, of which the y component expresses the amplitude of a harmonic oscillation.PhiJ said:Haven't heard of a phasor. By the hyperphysics website, do you mean hyperphysics.phy-astr.gsu.edu?
The wave equation is a mathematical formula that describes the behavior of waves, such as sound waves or light waves. It is often written as U = A sin(kx-wt), where U is the amplitude vector, A is the amplitude, k is the wave number, x is the position, and wt is the angular frequency multiplied by time.
The amplitude vector, denoted as U, represents the maximum displacement of any point on a wave from its equilibrium position. In other words, it measures the height or strength of the wave at a given point.
The amplitude vector, U, is directly proportional to the amplitude, A. This means that as the amplitude increases, so does the amplitude vector. However, the amplitude vector also takes into account the direction of the wave, whereas the amplitude only measures the magnitude of the wave.
The wave number, k, is a constant that represents the number of waves per unit distance. It is directly related to the wavelength of the wave, with a shorter wavelength resulting in a larger wave number. The wave number is also used to calculate the speed of the wave.
The wave equation is used in various fields of science and engineering, such as acoustics, optics, and electromagnetics. It is used to understand and predict the behavior of waves in different mediums, such as air, water, and solids. It is also used in the development of technologies, such as radar, sonar, and medical imaging.