Wave snapshot and displacement matching

Steps:

• Note y = y1 at x = λ/8 from the graph of the transverse wave profile.
• Trace the curve: after x = λ/8, the wave reaches the peak and descends to cross y = y1 again at x = 3λ/8.
• The wave then goes to the trough and ascends, crossing y = y1 at x = 7λ/8 within the wavelength.
• Confirm no other crossings between these points, as per sinusoidal periodicity.

Why B is correct:

• For a sinusoidal wave y = A sin(2πx/λ + φ), the phase φ yields solutions at x = 3λ/8 and 7λ/8 for y = y1 after x = λ/8, matching the graph's profile.

Why the others are wrong:

• A: Includes 5λ/8, where y = -y1 in the negative half-cycle.
• C: Both positions 5λ/8 and 7λ/8 occur where y ≠ y1 simultaneously.
• D: Repeats the given x = λ/8, ignoring "next" values.

Final answer: B