In a pure sine wave, the maximum amplitude occurs at two specific points: when the particle velocity is at its maximum and when the instantaneous pressure is at its maximum.
Let's consider a simple harmonic motion represented by a pure sine wave. In this motion, a particle oscillates back and forth around its equilibrium position. The displacement of the particle from its equilibrium position can be described by a sine function.
The particle velocity represents the rate of change of displacement with respect to time. At the points where the displacement is maximum, the particle velocity is zero because the particle momentarily comes to rest before changing direction. Therefore, the maximum amplitude of the sine wave corresponds to zero particle velocity.
On the other hand, the instantaneous pressure is related to the amplitude of the wave. In a sound wave, for example, the pressure variations create compressions and rarefactions in the medium through which the wave is traveling. At the points where the displacement is maximum, the pressure is also at its maximum. This occurs when the particle is at the extremes of its motion, creating regions of high pressure (compression) or low pressure (rarefaction) in the medium.
In summary, in a pure sine wave, the maximum amplitude corresponds to zero particle velocity, and the maximum instantaneous pressure occurs when the displacement is maximum.