1. What is the Speed of Sound Formula?

The speed of sound formula calculates how fast sound waves travel through a gas medium. 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 travels faster in lighter gases, at higher temperatures, and in gases with higher specific heat ratios.

3. Importance of Speed of Sound Calculation

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

4. Using the Calculator

Tips: Enter the adiabatic index (γ), gas constant (typically 8.314 J/mol·K), temperature in Kelvin, and molar mass in kg/mol. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical adiabatic index value?
A: For diatomic gases like air, γ is approximately 1.4. For monatomic gases like helium, it's about 1.67.

Q2: Why does temperature affect sound speed?
A: Higher temperature increases molecular motion and the speed at which pressure disturbances propagate through the medium.

Q3: How does molar mass affect sound speed?
A: Sound travels faster in gases with lower molar mass because lighter molecules can move more quickly in response to pressure changes.

Q4: What is the speed of sound in air at room temperature?
A: Approximately 343 m/s at 20°C (293 K) with γ = 1.4 and M = 0.029 kg/mol for air.

Q5: Does this formula work for liquids and solids?
A: No, this formula is specifically for ideal gases. Different formulas are used for liquids and solids where different elastic properties dominate.