Standing waves in a closed-open pipe

Steps:

• Boundary conditions require a node at the closed end and an antinode at the open end.
• Pipe length L equals an odd multiple of quarter-wavelengths: L = (2n-1)λ/4, where n=1,2,3,...
• Rearrange for wavelength: λ = 4L/(2n-1).
• For n=2, λ=4L/3, matching option C.

Why C is correct:

• λ=4L/3 is the first overtone (n=2) for a closed pipe, satisfying the node-antinode conditions.

Why the others are wrong:

• A: 2L/3 implies even multiple of λ/4, violating odd-quarter rule for closed pipes.
• B: L implies L=λ, or four quarter-waves (even multiple), not possible.
• D: 2L implies L=λ/2, or half-wave, incompatible with closed-end node.

Final answer: C