Final answer:
The maximum displacement amplitude of a standing wave, given that the displacement is √2 mm at certain points, is 2mm, extrapolated using properties of right triangles and the fact that nodes and antinodes create specific displacement patterns.
Therefore the correct answer is option A) 2mm.
Step-by-step explanation:
The question pertains to the concept of standing waves on a string and how the amplitude relates to the points of the string with specific displacements. The points where the displacement equals √2 mm are given as being separated by 15.0 cm, which suggests that these points are at positions where the amplitude of the wave is reduced by a factor of √2 due to the presence of nodes or antinodes.
Sine waves reflecting in a string fixed at both ends create standing waves with nodes and antinodes. The maximum displacement amplitude is found at the antinodes. Since the given displacement is the amplitude reduced by √2, and since √2 is the factor that relates the length of the diagonal of a square to its side (in this case, relating maximum amplitude to given displacement at other points), we can apply Pythagoras's theorem or properties of triangles to deduce that the maximum amplitude is twice the given displacement. Therefore, the correct answer is A) 2mm.