Stationary Waves in Pipes

Steps:

• Progressive waves reflect at pipe ends, interfering to form stationary waves if path difference is integer multiple of λ/2.
• For closed pipe P (one end closed), stationary waves form if L = (2n-1)λ/4, n=1,2,...
• For open pipe Q (both ends open), stationary waves form if L = nλ/2, n=1,2,...
• Given λ=20 cm and pipe lengths (as shown), both satisfy the conditions for fundamental or harmonic modes.

Why A is correct:

• Both pipes match the resonance length conditions for stationary wave formation per end-reflection interference.

Why the others are wrong:

• B: Q also resonates, as its length fits open pipe harmonics.
• C: P resonates, as its length fits closed pipe odd multiples of λ/4.
• D: Both pipes allow stationary waves based on given lengths.

Final answer: A