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30 Δεκ 2020 · Probably the simplest kind of wave is a transverse sinusoidal wave in a one-dimensional string. In such a wave each point of the string undergoes a harmonic oscillation. We will call the displacement from equilibrium \(u\), then we can plot \(u\) as a function of position on the string at a given point in time, Figure 9.2.1a, which is a ...
- 16.3: Mathematics
Equation \ref{16.6} is the linear wave equation, which is...
- 16.3: Mathematics
Equation \ref{16.6} is the linear wave equation, which is one of the most important equations in physics and engineering. We derived it here for a transverse wave, but it is equally important when investigating longitudinal waves.
In physics, a transverse wave is a wave that oscillates perpendicularly to the direction of the wave's advance. In contrast, a longitudinal wave travels in the direction of its oscillations.
In a transverse wave, the atoms of the medium move perpendicular to the direction that the energy is moving through the medium. When the wave has passed, the atoms of the medium have returned to their equilibrium positions. All transverse waves share certain characteristics. Waves have an amplitude (A). The amplitude is how far from equilibrium ...
A simple transverse wave can be represented by a sine or cosine curve, so called because the amplitude of any point on the curve— i.e., its distance from the axis—is proportional to the sine (or cosine) of an angle. In the figure, sine curves of various amplitudes are shown.
We derived it here for a transverse wave, but it is equally important when investigating longitudinal waves. This relationship was also derived using a sinusoidal wave, but it successfully describes any wave or pulse that has the form [latex] y(x,t)=f(x\mp vt).
Equation 16.6 is the linear wave equation, which is one of the most important equations in physics and engineering. We derived it here for a transverse wave, but it is equally important when investigating longitudinal waves.
