Xamine Conceptual Example 3 before addressing this question. A wave moves on a string with a constant velocity. Does this mean that the particles of the string always have zero acceleration?

No, the particles of the strings will not have zero acceleration.

Explanation:

Any wave motion through a string will travel in simple harmonic motion and not in linear motion. If the wave was moving in linear motion, then the acceleration of the particles of strings can be zero.

But here the significance of simple harmonic motion is that the acceleration cannot be zero. So even though the wave particles are moving in constant velocity on the string, the motion will be in simple harmonic mode.

So, the vector addition will not be zero. Thus, the particles will not exhibit zero acceleration even though they have constant velocity due to simple harmonic motion.