1. What is the Speed of Sound Formula?

The speed of sound formula calculates the speed at which sound waves propagate through 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 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 gases with lower molar mass, higher temperatures, and higher adiabatic indices.

3. Importance of Speed of Sound Calculation

Details: Calculating the speed of sound is essential in various fields including acoustics, meteorology, aerospace engineering, and chemical processing for designing systems and predicting wave behavior.

4. Using the Calculator

Tips: Enter the adiabatic index, gas constant (default is 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 the typical value for adiabatic index (γ)?
A: For monatomic gases (helium, argon), γ = 1.67. For diatomic gases (air, nitrogen, oxygen), γ = 1.4. For polyatomic gases, values vary.

Q2: Why does temperature affect sound speed?
A: Higher temperature increases the average molecular speed and collision frequency, allowing sound waves to propagate faster 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 and respond to pressure changes more quickly.

Q4: Is this formula accurate for real gases?
A: The formula provides good approximations for ideal gases at moderate temperatures and pressures. For real gases, corrections may be needed.

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.