1. What is the Speed of Sound Equation?

The speed of sound equation calculates the velocity at which sound waves propagate 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 (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 in acoustics, aerodynamics, meteorology, and various engineering applications where wave propagation through gases is studied.

4. Using the Calculator

Tips: Enter adiabatic index (unitless), gas constant in 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 value for adiabatic index (γ)?
A: For diatomic gases like air, γ is approximately 1.4. For monatomic gases it's 1.67, and for polyatomic gases it ranges from 1.1 to 1.33.

Q2: What is the universal gas constant value?
A: The universal gas constant R is approximately 8.314 J/mol·K.

Q3: How does temperature affect sound speed?
A: Sound speed increases with the square root of absolute temperature. For air, sound speed increases by about 0.6 m/s per degree Celsius.

Q4: Why does sound travel faster in lighter gases?
A: Sound speed is inversely proportional to the square root of molar mass. Lighter gas molecules can transmit vibrational energy more quickly.

Q5: 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, R=8.314 J/mol·K, and M=0.029 kg/mol for air.