Question

A certain organ pipe, open at both ends, produces a fundamental frequency of 297 Hz in air. Part A If the pipe is filled with helium at the same temperature, what fundamental frequency fHe will it produce? Take the molar mass of air to be 28.8 g/mol and the molar mass of helium to be 4.00 g/mol. Express your answer in hertz. V ALD O O ? file Submit Request Answer

Answer 1

Sol::

Given data:

fundamental frequency= 297 Hz

molar mass of air = 28.8 g/mol
the molar mass of helium =4.00 g/mol

Let ρ = density.

γ(air) = 1.4 and γ(He) = 5/3

Sound velocity c = √(γ*pressure/ρ)

As Frequency f is proportional to c, and pressure is the same in both cases, thus

f(He) = f(air) * √[(γ(He)/γ(air)) * (ρ(air)/ρ(He))]

= 297 * sqrt[(5/3)/1.4 * 28.8/4]
= 869.52 Hz

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