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Speed of Sound Equation:
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The speed of sound formula calculates the speed at which sound waves propagate through a medium. For ideal gases, it is given by \( v = \sqrt{\frac{\gamma R T}{M}} \), where γ is the adiabatic index, R is the gas constant, T is the absolute temperature, and M is the molar mass of the gas.
The calculator uses the speed of sound equation:
Where:
Explanation: The equation shows that sound speed increases with temperature and decreases with molecular mass of the gas. The adiabatic index represents how the gas responds to compression.
Details: Calculating sound speed is essential in various fields including acoustics, aerodynamics, meteorology, and engineering. It helps in designing audio systems, studying atmospheric conditions, and understanding gas properties.
Tips: Enter the adiabatic index (γ), gas constant (R), temperature in Kelvin (T), and molar mass (M). All values must be positive. The gas constant is typically 8.314 J/mol·K for ideal gases.
Q1: What is the adiabatic index (γ)?
A: The adiabatic index is the ratio of specific heats (Cp/Cv) of a gas. For air, it's approximately 1.4; for monatomic gases like helium, it's 1.67.
Q2: Why does temperature affect sound speed?
A: Higher temperature increases molecular motion, allowing sound waves to propagate faster through the medium.
Q3: How does molar mass affect sound speed?
A: Heavier molecules move more slowly, resulting in slower sound propagation. Lighter gases like helium have higher sound speeds.
Q4: Is this formula valid for all media?
A: No, this formula is specifically for ideal gases. Sound speed in liquids and solids is calculated using different formulas involving bulk modulus and density.
Q5: What is a typical speed of sound in air?
A: At 20°C (293K), sound travels at approximately 343 m/s in air with γ=1.4, R=8.314 J/mol·K, and M=0.029 kg/mol.