A pipe open at both ends has fundamental frequency f. The pipe is placed vertically into water until half its length is submerged. What is the new fundamental frequency of the remaining air column?
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Question

A pipe open at both ends has fundamental frequency f. The pipe is placed vertically into water until half its length is submerged. What is the new fundamental frequency of the remaining air column?

G1 Physics · Accepted Answer

Step 1: Original pipe length is L; open at both ends, its fundamental is f = v/(2L). Step 2: Submerging half the pipe leaves an air column of length L/2, open at the upper end and effectively closed by water at the lower end. Step 3: A closed–open air column has fundamental f′ = v/(4Lₐᵢᵣ). Step 4: Substitute Lₐᵢᵣ = L/2: f′ = v/[4(L/2)] = v/(2L). Step 5: Thus f′ = f. Final answer: The new frequency is f, Option B.