Phase Difference via Time Shift in Wave Graphs

Steps:

• Determine the period T of the waves from one full cycle on the graph (e.g., from peak to peak).
• Identify the time shift δt between corresponding points, such as zero crossings or maxima, on the two displacement curves at P.
• Calculate phase difference φ = (360° × δt / T).
• For the given graph, δt = (3/8)T, so φ = 360° × (3/8) = 135°.

Why C is correct:

• Phase difference is defined as the angular shift φ = 2π (δt / T) radians or 360° (δt / T), matching 135° for the observed time delay.

Why the others are wrong:

• A: Requires δt = T/8 (45° shift), but graph shows larger 3T/8 delay.
• B: Requires δt = T/4 (90° shift), but delay exceeds quarter period.
• D: Requires δt = T/2 (180° shift), but delay is less than half period.

Final answer: C