To determine when standing waves occur, let's carefully consider the different conditions listed in the multiple-choice options.
1. Option A: There are two identical waves travelling in opposite directions:
- Standing waves are typically formed when two waves of the same frequency and amplitude travel in opposite directions and interfere with each other. This condition is essential for the creation of standing waves. Therefore, option A is correct.
2. Option B: There are an integer number of loops:
- Standing waves are characterized by nodes (points of no displacement) and antinodes (points of maximum amplitude). For a standing wave to be formed, the length of the medium must allow the wave pattern to fit into it, creating an integer number of half-wavelengths (or loops). Thus, option B is also correct.
3. Option C: Two waves overlap and interfere:
- The formation of standing waves is a direct result of the interference between two waves overlapping equally and oppositely. This interference is called constructive and destructive interference at certain points, leading to the creation of standing waves. Thus, option C is correct as well.
4. Option D: All of the above:
- Since standing waves require all the conditions described in options A, B, and C, option D is inclusive and correct. Therefore, standing waves only occur when all the above conditions are met.
Hence, standing waves only occur under the conditions listed in all of the correct options above. As a result, the best choice is:
D) All of the above
