1. What is the Speed of Sound Equation?

The speed of sound equation calculates how fast sound waves travel through a medium. For ideal gases, it's given by \( v = \sqrt{\frac{\gamma R T}{M}} \), where γ is the adiabatic index, R is the gas constant, T is temperature, and M is molar mass.

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 specific heat ratios.

3. Importance of Sound Speed Calculation

Details: Calculating sound speed is crucial for acoustics engineering, atmospheric studies, medical ultrasound applications, and designing audio equipment and concert halls.

4. Using the Calculator

Tips: Enter the adiabatic index (γ), gas constant (R), temperature in Kelvin, and molar mass. All values must be positive. For air at room temperature, typical values are γ=1.4, R=8.314, T=298, M=0.029.

5. Frequently Asked Questions (FAQ)

Q1: What is the adiabatic index (γ)?
A: The adiabatic index is the ratio of specific heats (Cp/Cv) and varies by gas. For monatomic gases it's 1.67, for diatomic gases 1.4.

Q2: Why temperature in Kelvin?
A: The gas equation requires absolute temperature, making Kelvin the appropriate unit as it starts from absolute zero.

Q3: How does sound speed change with altitude?
A: Sound speed decreases with altitude due to lower temperatures, despite the decrease in air density.

Q4: Does humidity affect sound speed?
A: Yes, humid air has slightly lower molar mass than dry air, which increases sound speed by about 0.1-0.5%.

Q5: What's the speed of sound in water?
A: Approximately 1480 m/s, but this equation doesn't apply to liquids which have different acoustic properties.