Phase Relationships in Stationary Waves

Steps:

• Stationary waves on a fixed string have nodes at ends P and T, with antinodes between.
• The displacement function y(x,t) = 2A sin(kx) cos(ωt) shows phase determined by the cos(ωt) term, uniform across the string.
• Points Q and S, as antinodes with sin(kx) of the same sign, oscillate with the same phase.
• Energy in stationary waves oscillates locally without net transfer.

Why B is correct:

• In standing waves, points like Q and S at symmetric antinodes share the same phase via the uniform cos(ωt) factor, oscillating in unison.

Why the others are wrong:

• A: Q is an antinode with maximum amplitude, not a node.
• C: Distance P to T equals nλ/2 for integer n; three full wavelengths implies n=6, but typical setups differ.
• D: Stationary waves trap energy between nodes, transferring none from P to T.

Final answer: B