1. What is the Speed of Sound Equation with Humidity?

The speed of sound in air varies with temperature and humidity. This calculator uses an empirical equation that accounts for both factors to provide a more accurate estimate than temperature-only formulas.

2. How Does the Calculator Work?

The calculator uses the following equation:

Where:

• \( v \) — Speed of sound (m/s)
• \( T \) — Temperature (°C)
• \( H \) — Relative humidity (%)

Explanation: The equation shows that sound travels faster in warmer air and more humid air, though the temperature effect is more significant.

3. Importance of Humidity in Sound Speed

Details: While temperature is the primary factor affecting sound speed, humidity has a measurable effect, especially in warm conditions. The speed increases with humidity because water molecules are lighter than nitrogen and oxygen molecules.

4. Using the Calculator

Tips: Enter temperature in Celsius and relative humidity as a percentage (0-100%). The calculator is valid for typical atmospheric conditions near sea level.

5. Frequently Asked Questions (FAQ)

Q1: Why does humidity affect sound speed?
A: Humid air is less dense than dry air at the same temperature because water molecules (H₂O) are lighter than nitrogen (N₂) and oxygen (O₂) molecules.

Q2: How significant is the humidity effect?
A: At 20°C, changing humidity from 0% to 100% increases sound speed by about 1.24 m/s, compared to a 12.1 m/s increase from 0°C to 20°C at constant humidity.

Q3: What are typical sound speeds?
A: At 20°C with 50% humidity: ~343 m/s; at 0°C with 0% humidity: ~331 m/s; at 30°C with 80% humidity: ~349 m/s.

Q4: Does this equation work for all conditions?
A: It's valid for normal atmospheric conditions. For extreme temperatures, high altitudes, or other gases, different equations are needed.

Q5: How does this compare to the standard speed of sound formula?
A: The standard formula v = 331 + 0.6T only accounts for temperature. This version adds humidity correction for greater accuracy.