In an organ pipe with one end at x = 0, the pressure is p = p₀ cos(3πx/2) sin(300πt), where x is in metres and t in seconds. Which description of the pipe is possible?
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In an organ pipe with one end at x = 0, the pressure is p = p₀ cos(3πx/2) sin(300πt), where x is in metres and t in seconds. Which description of the pipe is possible?

G1 Physics · Accepted Answer

Step 1: p = p₀ cos(kx) sin(ωt) with k=3π/2 m⁻¹. At x=0 pressure is an antinode, so x=0 is a closed end. Step 2: A closed end also occurs where cos(kL)=±1. For L=2 m, kL=3π, so the far end is closed. Final: C.