Speed Of Sound Height Calculator

Speed of Sound at Height Formula:

\[ v = \sqrt{\frac{\gamma R T}{M}} \]

Adiabatic Index (γ):

unitless

Gas Constant (R):

J/mol·K

Temperature (T):

Molar Mass (M):

kg/mol

Speed of Sound (v):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Speed of Sound at Height Formula?

The speed of sound at height formula calculates the speed of sound in a gas based on temperature, molar mass, and gas properties. It accounts for how temperature decreases with height in the atmosphere, affecting sound propagation.

2. How Does the Calculator Work?

The calculator uses the speed of sound formula:

\[ v = \sqrt{\frac{\gamma R T}{M}} \]

Where:

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

Explanation: The equation shows that sound speed increases with temperature and decreases with molar mass of the gas. Temperature typically decreases with height in the atmosphere, reducing sound speed at higher altitudes.

3. Importance of Speed of Sound Calculation

Details: Calculating sound speed at different heights is crucial for atmospheric studies, aviation, acoustic engineering, and understanding how sound propagates through different atmospheric layers.

4. Using the Calculator

Tips: Enter the adiabatic index (typically 1.4 for air), gas constant (8.314 J/mol·K for ideal gases), temperature in Kelvin, and molar mass in kg/mol (0.02897 kg/mol for air). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why does temperature decrease with height affect sound speed?
A: Sound speed is proportional to the square root of temperature. As temperature decreases with height, sound waves travel slower at higher altitudes.

Q2: What is the typical speed of sound in air at sea level?
A: Approximately 343 m/s at 20°C (293 K) with standard atmospheric conditions.

Q3: How does humidity affect sound speed?
A: Humidity slightly increases sound speed because water vapor has lower molar mass than dry air, effectively reducing the average molar mass of the air mixture.

Q4: Can this formula be used for liquids?
A: No, this formula is specifically for ideal gases. Sound speed in liquids follows different physical principles and requires different equations.

Q5: Why is the adiabatic index important?
A: The adiabatic index (γ) represents the ratio of specific heats and accounts for how sound waves compress and expand the medium adiabatically (without heat transfer).