1. What is the Speed of Sound Equation?

The speed of sound equation calculates the speed at which sound waves propagate through a medium. For ideal gases, it depends on the adiabatic index, gas constant, temperature, and molar mass of the gas.

2. How Does the Calculator Work?

The calculator uses the speed of sound equation:

Where:

• \( v \) — Speed of sound (m/s)
• \( \gamma \) — Adiabatic index (unitless)
• \( R \) — Gas constant (8.314 J/mol·K)
• \( T \) — Temperature (K)
• \( M \) — Molar mass (kg/mol)

Explanation: The equation shows that sound speed increases with temperature and decreases with molecular mass of the gas.

3. Importance of Speed of Sound Calculation

Details: Calculating sound speed is crucial for acoustics, aerodynamics, meteorology, and various engineering applications where wave propagation through gases is important.

4. Using the Calculator

Tips: Enter adiabatic index (γ), gas constant (R), temperature in Kelvin (T), and molar mass in kg/mol (M). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the adiabatic index (γ)?
A: The adiabatic index is the ratio of specific heats (Cp/Cv) and varies with molecular structure (1.67 for monatomic, 1.4 for diatomic gases).

Q2: Why temperature in Kelvin?
A: The gas constant R is defined using Kelvin scale, and absolute temperature is required for thermodynamic calculations.

Q3: How does sound speed vary with temperature?
A: Sound speed increases with square root of absolute temperature. For air, it increases by about 0.6 m/s per °C.

Q4: What are typical sound speeds in common gases?
A: ~343 m/s in air at 20°C, ~1284 m/s in hydrogen, ~972 m/s in helium, ~267 m/s in carbon dioxide.

Q5: Does this equation work for liquids and solids?
A: No, this equation is for ideal gases. Different equations are used for liquids and solids based on bulk modulus and density.