Standing Wave Characteristics on a String

Steps:

• Standing waves form from interference of two identical waves traveling in opposite directions, creating nodes (zero displacement) and antinodes (maximum displacement).
• Nodes remain stationary; between nodes, the string vibrates with varying phase.
• At instants when the wave is at rest (zero velocity everywhere), the entire segment between nodes flattens to horizontal.
• Evaluate options: A matches rest position; B, C, D contradict phase and count properties.

Why A is correct:

• In standing waves, at times when all points pass through equilibrium (like t=0 in sinusoidal description), the string between nodes has zero displacement, appearing horizontal per the wave equation y(x,t)=0 for all x at those t.

Why the others are wrong:

• B: Points between antinodes have varying amplitudes, maximum only at antinodes.
• C: Nodes exceed antinodes by one in a finite string fixed at both ends.
• D: Adjacent antinodes are out of phase by 180 degrees.

Final answer: A