Final Answer:
A wave on a string moving to the right,. At the very next instant in time, the direction of the velocity of a particle at the point will be rightward (option C).
Step-by-step explanation:
In a wave on a string, the motion of individual particles is influenced by the wave's characteristics. At point a, the wave is moving to the right, and the particles at that point are oscillating vertically.
The velocity of a particle in a wave is perpendicular to the wave itself, and it is in the direction of the wave propagation. In this case, as the wave is moving to the right, the particle at point a will have a velocity directed to the right.
The motion of particles in a transverse wave, like the one on the string, is crucial to understanding wave dynamics. In this context, the wave's energy is transferred through the motion of particles, and their velocities are aligned with the direction of wave propagation. Therefore, at point a, the velocity of the particle is rightward (option C).