How Does Helium Affect the Fundamental Frequency of an Organ Pipe?

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SUMMARY

The fundamental frequency of an organ pipe filled with helium is determined by the speed of sound in the gas. In this case, the speed of sound in helium is 999 m/s, while in air it is 344 m/s. The relationship between the speed of sound and the fundamental frequency can be expressed using the formula fn = n v / 2 L, where 'n' is the harmonic number and 'L' is the length of the pipe. The molar mass of the gases plays a crucial role in calculating the density, which directly affects the speed of sound.

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  • Understanding of wave mechanics and sound propagation
  • Familiarity with the ideal gas law
  • Knowledge of the relationship between density and molar mass
  • Basic proficiency in solving equations involving frequency and wavelength
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Physics students, acoustics researchers, and anyone interested in the properties of sound in different gases, particularly in musical acoustics and organ pipe design.

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Homework Statement


A certain organ pipe, open at both ends, produces a fundamental frequency of 275 Hz 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 28.8 g/mol and the molar mass of helium to be 4.00 g/mol.


Homework Equations



below

The Attempt at a Solution


v(he)=999 m/s
v(O)=344 m/s
I solved with [tex]fn = n v / 2 L[/tex] but I am not getting as accurately of an answer as id like. How can I incorporate the molar mass into these equations?
 
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You'll need to find the relationship between the speed of sound in an ideal gas to the density of the gas. The density is proportional to the molar mass.
 
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