A certain organ pipe, open at both ends, produces a fundamental frequency of 287

Question

A certain organ pipe, open at both ends, produces a fundamental frequency of 287Hz in air.If the pipe is filled with helium at the same temperature, what fundamental frequency f will it produce? Take the molar mass of air to be 28.8g/mol and the molar mass of helium to be 4.00g/mol . A certain organ pipe, open at both ends, produces a fundamental frequency of 287Hz in air.If the pipe is filled with helium at the same temperature, what fundamental frequency f will it produce? Take the molar mass of air to be 28.8g/mol and the molar mass of helium to be 4.00g/mol .

Explanation / Answer

Let ? = density.
?(air) = 1.4, ?(He) = 5/3
Sound velocity c = sqrt(?*pressure/?) (see the ref.)
Frequency f is proportional to c, and pressure is the same in both cases, thus
f(He) = f(air) * sqrt[(?(He)/?(air)) * (?(air)/?(He))]
= 287 * sqrt[(5/3)/1.4 * 28.8/4] = 840.25 Hz

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