Question

the diagram represents a snapshot in time of a wave traveling through a slinky. four locations along the slinky are labeled with a letter. indicate the direction of vibration of the slinky coils at these locations. location a tap here location b tap here location c tap here location d tap here

Explanation:

Step1: Recall Wave Vibration Rules

For a transverse wave (like on a Slinky shown as a sine wave), the direction of particle (coil) vibration is perpendicular to wave propagation. Assume the wave is moving, e.g., to the right (common case). At crests (A, B) and troughs (C, D), we analyze:

• Crests (A, B): At a crest, the coil is at the maximum upward displacement. If the wave is moving right, the crest's coil will move downward (toward equilibrium) next. Wait, no—wait, for transverse wave, the velocity of the particle: at a crest, the slope of the wave at that point (derivative) gives the direction. The formula for particle velocity in transverse wave: \( v_y = -v \frac{dy}{dx} \), where \( v \) is wave speed (positive in direction of propagation, say right, \( v>0 \)). At crest (A, B), \( \frac{dy}{dx} = 0 \)? No, wait, at crest, the slope changes from positive to negative. Wait, maybe simpler: for a wave moving to the right, the particles to the left of a crest are moving up, and to the right are moving down. At the crest (A, B), the particle is at the peak, so it will move downward (toward the equilibrium line). At troughs (C, D), the particle is at the bottom, so it will move upward (toward equilibrium).

Step2: Apply to Each Location

• Location A (Crest): If wave moves right, A is a crest. The coil at A will vibrate downward (toward the horizontal line).
• Location B (Crest): Same as A, downward.
• Location C (Trough): Trough, so coil vibrates upward (toward horizontal line).
• Location D (Trough): Same as C, upward.

(Note: If wave direction is left, the directions reverse, but typically, in such diagrams, wave direction is assumed right or we use the slope method. The key is that crests move down, troughs move up in transverse wave particle motion.)

Answer:

• Location A: Downward
• Location B: Downward
• Location C: Upward
• Location D: Upward

(Assuming wave propagates to the right; if wave direction is left, reverse: A and B upward, C and D downward. But the standard analysis for transverse wave particle velocity at crests/troughs: at crest, particle velocity is downward (if wave right), at trough, upward.)