Conditions for Forming Standing Waves

Steps:

• Stationary waves form from superposition of two waves traveling in opposite directions.
• For constructive and destructive interference to create nodes and antinodes, waves must match in key properties.
• Equal frequencies ensure interference patterns remain fixed in space.
• Equal speeds and wavelengths guarantee phase consistency and prevent pattern drift.

Why C is correct:

• Standing waves require identical speeds, frequencies, and wavelengths for perfect superposition, as per the wave interference principle where the resultant wave amplitude is stationary.

Why the others are wrong:

• A: Different speeds cause varying phase velocities, preventing fixed nodes.
• B: Different frequencies lead to beating, not stationary patterns.
• D: Different speeds and frequencies disrupt consistent interference.

Final answer: C