Two waves, both of amplitude A, are traveling in opposite directions along a rope. What is the range of displacement y that the two waves may cause when they overlap?
A. -2A ≤ y ≤ 2A
B. -A ≤ y ≤ A
C. -1/2A ≤ y ≤ 1/2A
D. 0 ≤ y ≤ A
(Honestly not sure how to solve this but I think the answer's A...)
you solve it by adding A sinTheta+AsinThetaA=2A SinTheta, which ranges from -2A t0 2A
Thank you. :)
To solve this problem, let's consider the two waves traveling in opposite directions along the rope. When the two waves overlap, their displacements at any point add up to give the overall displacement.
The maximum displacement occurs when the peaks of the waves line up, creating constructive interference. In this case, the two wave amplitudes add up to give the maximum displacement. The minimum displacement occurs when the peaks of one wave align with the troughs of the other wave, creating destructive interference. In this case, the two wave amplitudes cancel out, resulting in the minimum displacement.
Given that both waves have an amplitude of A, the maximum displacement occurs when the two wave amplitudes add up to give the maximum possible displacement, which is 2A. This corresponds to the two waves creating constructive interference.
On the other hand, the minimum displacement occurs when the two wave amplitudes cancel out, resulting in zero displacement.
Therefore, the range of displacement y that the two waves may cause when they overlap is from the minimum displacement (0) to the maximum displacement (2A). So, the correct answer is:
A. -2A ≤ y ≤ 2A