1. What is the Speed of Sound Formula?

The speed of sound formula calculates the speed at which sound waves propagate through a medium. For ideal gases, it is given by \( v = \sqrt{\frac{\gamma R T}{M}} \), where γ is the adiabatic index, R is the gas constant, T is the absolute temperature, and M is the molar mass of the gas.

2. How Does the Calculator Work?

The calculator uses the speed of sound formula:

Where:

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

Explanation: The formula shows that sound speed increases with temperature and decreases with molecular mass of the gas.

3. Importance of Speed of Sound Calculation

Details: Calculating sound speed is crucial for various applications including acoustics, meteorology, aerospace engineering, and medical ultrasound imaging.

4. Using the Calculator

Tips: Enter the adiabatic index (typically 1.4 for air), gas constant (8.314 J/mol·K), 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 at room temperature?
A: Approximately 343 m/s at 20°C (293 K) for dry air.

Q2: How does humidity affect sound speed?
A: Humidity slightly increases sound speed as water vapor has lower molar mass than dry air components.

Q3: Why is temperature in Kelvin used?
A: The formula requires absolute temperature because it's derived from kinetic theory where temperature is proportional to molecular kinetic energy.

Q4: What are typical γ values for common gases?
A: Air: 1.4, Helium: 1.66, Carbon dioxide: 1.3, Argon: 1.67

Q5: Does this formula work for liquids and solids?
A: No, this formula is specific to ideal gases. Sound speed in liquids and solids is calculated using different formulas involving bulk modulus and density.