No, a phase shift in a sine wave does not imply that the wave is moving faster than another wave. The speed of a wave refers to how quickly the shape or pattern of the wave propagates through space, while the phase shift refers to a change in the starting point or position of the wave.
When two identical sine waves are moving to the right and one of them experiences a phase shift to the right, it means that the wave's starting point or position has been shifted in that direction. However, the speed of propagation for both waves remains the same.
In other words, the phase shift affects the initial alignment of the wave but does not alter the speed at which the wave travels. The speed of propagation of a wave is determined by its wavelength and frequency, not by the phase shift.