1. What is the Speed of Sound Formula?

Definition: This formula calculates the speed at which sound waves propagate through a gas based on its thermodynamic properties.

Purpose: It helps physicists, engineers, and meteorologists understand sound propagation in different gases under various conditions.

2. How Does the Formula Work?

The formula is:

Where:

• \( v \) — Speed of sound (m/s)
• \( \gamma \) — Adiabatic index (unitless)
• \( R \) — Universal gas constant (8.314 J/mol·K)
• \( T \) — Absolute temperature (Kelvin)
• \( M \) — Molar mass of the gas (kg/mol)

Explanation: The speed depends on how quickly molecules can transfer vibrations (related to temperature and molecular weight) and the gas's ability to compress (adiabatic index).

3. Importance of Speed of Sound Calculation

Details: Accurate speed calculations are crucial for designing acoustic systems, atmospheric studies, and industrial applications like ultrasonic testing.

4. Using the Calculator

Tips: Enter the adiabatic index (γ = 1.4 for air), temperature in Kelvin (293.15K = 20°C), and molar mass (0.02896 kg/mol for air). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical adiabatic index for air?
A: For dry air at standard conditions, γ ≈ 1.4. For diatomic gases like N₂ and O₂, it's typically 1.4, while monatomic gases like Ar have γ ≈ 1.67.

Q2: How do I convert Celsius to Kelvin?
A: Add 273.15 to the Celsius temperature. For example, 20°C = 293.15K.

Q3: What's the molar mass of air?
A: Approximately 0.02896 kg/mol for dry air (78% N₂, 21% O₂, 1% Ar).

Q4: Does humidity affect the speed of sound?
A: Yes, water vapor changes both the average molar mass and γ. The effect is small but measurable.

Q5: Why does sound travel faster in helium?
A: Helium has lower molar mass (0.004 kg/mol) and higher γ (1.66), both increasing the speed of sound compared to air.