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coverband
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In the wave equation u(x,t), what does u represent?
coverband said:yungman: u''(t)=u''(x)c^2
lckurtz: so visually its like a plane/surface in 3D (x,y,z) where x = x, y = t and z = u ...?
coverband said:yungman: u''(t)=u''(x)c^2
lckurtz: so visually its like a plane/surface in 3D (x,y,z) where x = x, y = t and z = u ...?
Your original equation did not have a "y" variable so you can think of z as either the height of a string in one-dimension or as the height of a "cylindrical" wave, extending infinitely in the y direction. In any case, your original "u" is the height of the wave if you are thinking of a physical wave, the intensity if you are thinking of a light wave, etc.coverband said:Anyone else so visually its like a plane/surface in 3D (x,y,z) where x = x, y = t and z = u ...? !
coverband said:In the wave equation u(x,t), what does u represent?
The wave equation is a mathematical formula that describes how waves propagate through a medium. It is used to model a variety of physical phenomena, such as sound waves, electromagnetic waves, and water waves.
The variable u in the wave equation represents the displacement of the wave at a specific point in space and time. It is a function of both the position, x, and time, t.
The wave equation is derived from the laws of motion and the conservation of energy. It can also be derived from Maxwell's equations, which describe the behavior of electromagnetic waves.
The units of u in the wave equation depend on the type of wave being modeled. For example, in the case of a sound wave, u would have units of pressure or displacement. In the case of an electromagnetic wave, u would have units of electric or magnetic field strength.
The variable u in the wave equation is the solution to the equation and represents the amplitude of the wave at a given point in space and time. It is essential in understanding the behavior and propagation of waves in a medium.