This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
You're on a roll — Step 1: Analyze the starting positions of waves P and Q at t=0. Wave P starts at its maximum positive displacement at t=0. This corresponds to the peak of a cosine function. Wave Q starts at zero displacement and is increasing at t=0. This corresponds to the start of a sine function. Step 2: Determine the phase of each wave relative to a standard sine wave. A standard sine wave, y = A ( t), has a phase of 0 at t=0. A wave that starts at its maximum positive displacement, like wave P, is equivalent to a sine wave shifted by (1)/(4) of a cycle (or ()/(2) radians) to the left. So, wave P has an initial phase of +()/(2) relative to wave Q. Step 3: Calculate the phase difference. The phase difference ( ) between wave P and wave Q is the difference in their initial phases. = Phase of P - Phase of Q = ()/(2) - 0 = ()/(2) Alternatively, observe that wave P is shifted by one-quarter of a wavelength (or period) relative to wave Q. Since one full cycle corresponds to 2 radians, a quarter cycle corresponds to: = (1)/(4) × 2 = ()/(2) Step 4: Compare with the given options. The calculated phase difference is ()/(2), which matches option A. The final answer is A. Got more? Send 'em!