Stationary waves in open pipes require integer half-wavelengths fitting the length

Steps:

• For a pipe open at both ends, stationary waves form when length L equals nλ/2, where n is a positive integer (harmonic number) and λ is wavelength.
• Rearrange to λ = 2L/n; here L=100 cm, so λ=200/n cm.
• Test options: n must be integer for resonance.
• A (50 cm) gives n=200/50=4 (integer); others do not.

Why A is correct:

• λ=50 cm satisfies L=nλ/2 with n=4, per the resonance condition for open pipes.

Why the others are wrong:

• B: λ=75 cm gives n=200/75≈2.67 (not integer, no resonance).
• C: λ=150 cm gives n=200/150≈1.33 (not integer, no resonance).
• D: λ=300 cm gives n=200/300≈0.67 (not integer, no resonance).

Final answer: A