1. What is the Speed of Sound?

Definition: The speed of sound is the distance traveled per unit time by a sound wave as it propagates through an elastic medium.

Purpose: This calculator determines the speed of sound in gases based on thermodynamic properties.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( v \) — Speed of sound (m/s)
• \( \gamma \) — Adiabatic index (ratio of specific heats, 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 thermodynamic properties (γ).

3. Importance of Speed of Sound Calculations

Details: Used in acoustics, aerodynamics, meteorology, and engineering applications like ultrasonic testing and aircraft design.

4. Using the Calculator

Tips:

• For air at 20°C (293.15K), typical values are γ=1.4, M=0.02897 kg/mol
• Temperature must be in Kelvin (K = °C + 273.15)
• Molar mass should be in kg/mol (divide g/mol by 1000)

5. Frequently Asked Questions (FAQ)

Q1: What's a typical γ value for common gases?
A: Air = 1.4, Helium = 1.66, Argon = 1.67, CO₂ = 1.28

Q2: Why does sound travel faster in helium?
A: Primarily because of helium's low molar mass (0.004 kg/mol) in the denominator of the equation.

Q3: How does temperature affect the speed?
A: Speed increases with temperature (∝√T) as molecules move faster and transfer vibrations more quickly.

Q4: Is this formula valid for liquids/solids?
A: No, this is specifically for ideal gases. Different formulas apply for other states of matter.

Q5: What's the speed of sound in air at room temperature?
A: About 343 m/s (using γ=1.4, T=293K, M=0.02897 kg/mol)