Question

Standing waves are formed on a string when interference occurs between two waves having

• A. the same amplitude travelling in the same direction with no phase difference between them
• B. the same amplitude, travelling in the opposite direction with no phase difference between them
• C. different amplitudes travelling in the same direction
• D. different amplitudes travelling in the opposite direction

Hint:

Standing waves are produced by interference of two identical waves travelling in opposite directions.

Answer 1

The Correct Option is B

Understanding Standing Waves:

Standing waves are a phenomenon that occurs due to the superposition of two waves traveling in opposite directions with the same frequency and amplitude. These waves interfere with each other to form a wave pattern that appears to be stationary, hence the name "standing wave".

Explanation of Options:

• Option 1: The same amplitude traveling in the same direction with no phase difference between them: This scenario will result in constructive interference but not standing waves, as standing waves require waves traveling in opposite directions.
• Option 2: The same amplitude, traveling in the opposite direction with no phase difference between them: This is the correct condition for creating standing waves. The interference of these waves causes nodes and antinodes to form, creating the appearance of a stationary wave pattern.
• Option 3: Different amplitudes traveling in the same direction: Waves with different amplitudes do not form standing waves due to imbalance, and being in the same direction doesn't meet the criteria for standing waves.
• Option 4: Different amplitudes traveling in the opposite direction: While travel directions are suitable, the differing amplitudes prevent the creation of a consistent node and antinode pattern, which is essential for standing waves.

Conclusion:

The correct choice is: the same amplitude, traveling in the opposite direction with no phase difference between them. This condition fulfills all the requirements for the formation of standing waves.