1. What is the Speed of Sound Formula?

The speed of sound formula 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 formula:

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 formula 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 essential in acoustics, aerodynamics, meteorology, and various engineering applications where wave propagation through gases is studied.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the typical value of γ for air?
A: For diatomic gases like air, γ is approximately 1.4.

Q2: Why does sound travel faster in warmer air?
A: Sound speed is proportional to the square root of temperature. Warmer air molecules move faster, allowing sound waves to propagate more quickly.

Q3: How does molar mass affect sound speed?
A: Sound speed is inversely proportional to the square root of molar mass. Lighter gases allow sound to travel faster.

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

Q5: Can this formula be used for liquids and solids?
A: No, this formula is specific to ideal gases. Different formulas are used for liquids and solids where bulk modulus and density are the key parameters.