1. What is the Speed of Sound Equation?

The speed of sound equation calculates the velocity at which sound waves propagate through a 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 adiabatic indices.

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 important.

4. Using the Calculator

Tips: Enter the adiabatic index (typically 1.4 for air), gas constant (8.314 J/mol·K for ideal gases), temperature in Kelvin, and molar mass in kg/mol. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical speed of sound in air?
A: At 20°C (293K), sound travels at approximately 343 m/s in air with γ=1.4 and molar mass of 0.029 kg/mol.

Q2: How does temperature affect sound speed?
A: Sound speed increases with temperature, as the equation shows a direct square root relationship with temperature.

Q3: Why does sound travel faster in helium?
A: Helium has a lower molar mass (0.004 kg/mol) compared to air (0.029 kg/mol), resulting in higher sound speed despite similar γ values.

Q4: What is the adiabatic index (γ)?
A: γ is the ratio of specific heats (Cp/Cv) and represents how a gas responds to compression. For monatomic gases γ=1.67, for diatomic gases γ=1.4.

Q5: Does this equation work for liquids and solids?
A: No, this specific equation is for ideal gases. Sound propagation in liquids and solids follows different formulas accounting for bulk modulus and density.