Transverse wave particle velocities oppose the local slope direction

Steps:

• Identify wave direction: rightward, so particle velocity $v_y = -v \frac{dy}{dx}$, where $v > 0$.
• For point 1 (positive slope, rising to right): $\frac{dy}{dx} > 0$, so $v_y < 0$ (downward).
• For point 2 (negative slope, falling to right): $\frac{dy}{dx} < 0$, so $v_y > 0$ (upward).
• For point 3 (positive slope, rising to right): $\frac{dy}{dx} > 0$, so $v_y < 0$ (downward).

Why D is correct:

• Matches $v_y = -v \frac{dy}{dx}$ for the snapshot's slopes at points 1 (down), 2 (up), and 3 (down).

Why the others are wrong:

• A: Horizontal arrows imply longitudinal motion, but string waves are transverse (vertical).
• B: Reverses directions, ignoring slope opposition in rightward wave.
• C: Identical to D, but listed separately—likely a duplicate error.

Final answer: D