1. What is the Speed of Sound Formula?

The speed of sound formula calculates the velocity at which sound waves propagate through a medium. For an ideal gas, 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 the speed of sound is essential in various fields including acoustics, aeronautics, meteorology, and engineering design. It helps in understanding wave propagation, designing sonic equipment, and studying atmospheric conditions.

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 numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the adiabatic index (γ)?
A: The adiabatic index is the ratio of specific heats (Cp/Cv) of a gas, which is unitless. For air, it's approximately 1.4.

Q2: Why is temperature in Kelvin?
A: The Kelvin scale is an absolute temperature scale where 0K represents absolute zero, making it appropriate for thermodynamic calculations.

Q3: How does molar mass affect sound speed?
A: Sound travels faster in gases with lower molar mass. This is why sound travels faster in helium than in air.

Q4: What is the speed of sound in air at room temperature?
A: Approximately 343 m/s at 20°C (293K) with γ=1.4, R=8.314 J/mol·K, and M=0.029 kg/mol for air.

Q5: Does this formula work for liquids and solids?
A: No, this specific formula is for ideal gases. Different formulas exist for liquids and solids based on their bulk modulus and density.