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 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 travels faster in lighter gases, at higher temperatures, and in gases with higher adiabatic indices.

3. Importance of Speed of Sound Calculation

Details: Calculating sound speed is crucial for various applications including acoustics engineering, atmospheric studies, medical ultrasound, and industrial process monitoring.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the typical value of γ for common gases?
A: For monatomic gases (He, Ar) γ = 1.67, for diatomic gases (N₂, O₂) γ = 1.4, and for polyatomic gases it varies.

Q2: Why does temperature affect sound speed?
A: Higher temperature increases molecular motion and collision frequency, allowing sound waves to propagate faster through the medium.

Q3: How does molar mass influence sound speed?
A: Sound travels faster in lighter gases because molecules can move and respond to pressure changes more quickly.

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: Does this formula work for liquids and solids?
A: No, this formula is specifically for ideal gases. Liquids and solids have different formulas based on bulk modulus and density.