Standing wave amplitude in closed tube

Steps:

• Identify closed end as displacement node (amplitude zero) and open end as antinode (maximum amplitude).
• For fundamental mode, tube length L equals quarter wavelength (λ/4).
• Displacement amplitude varies as a = A sin(πx / (2L)), starting at zero at x=0 and peaking at x=L.
• Match graph to this sinusoidal increase from node to antinode.

Why A is correct:

• Graph A depicts amplitude rising from zero at closed end to maximum at open end, consistent with sin(πx / (2L)) for λ=4L.

Why the others are wrong:

• B shows constant amplitude, ignoring node-antinode positions.
• C has maximum at closed end, contradicting displacement node there.
• D exhibits multiple peaks, suggesting higher harmonic not matching fundamental mode.

Final answer: A