The fundamental frequency of an open-open tube is 1500 Hz...

The fundamental frequency of an open-open tube is $1500 \mathrm{Hz}$ when the tube is filled with $0^{\circ} \mathrm{C}$ helium. What is its frequency when filled with $0^{\circ} \mathrm{C}$ air?

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Key Concepts

Standing Waves in Open-Open Tubes

In acoustic systems, an open-open tube supports standing waves with antinodes at both open ends. The fundamental frequency, or first harmonic, is established when the tube accommodates half of a wavelength, meaning the wavelength is twice the length of the tube. This concept is vital for connecting the physical dimensions of the tube to the resonant frequencies it supports.

Speed of Sound in Gases

The speed of sound in a gas is determined by the gas's intrinsic properties, including its temperature, molecular weight, and adiabatic index. It can be calculated using the formula v = ?(?RT/M), where v is the speed of sound, ? is the adiabatic constant, R is the universal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas. This relationship explains why gases like helium and air, even at the same temperature, exhibit different speeds of sound, thereby affecting the frequency of sound waves within a resonant system.

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