Explanation of the speed of sound waves in a gas by Ron Kurtus - Succeed in Understanding Physics. Key words: physical science, air, temperature, nitrogen, oxygen, water vapor, argon, carbon dioxide, pressure, equation, meters per second, Celsius, Fahrenheit, molecular mass, average velocity, School for Champions. Copyright © Restrictions
Speed of Sound in a Gas
by Ron Kurtus (revised 1 June 2008)
The speed of sound in a gas is primarily a function of its temperature. Air is a mixture of gases and includes water vapor. The relative humidity of air has a slight effect on the speed of sound, while changes in air pressure have no real effect on the speed.
A simple equation can be used to approximate the speed of sound. A more complex equation and can be used with other gases. The speed of sound in any gas takes into account other factors. The speed also is a specific fraction of the average speed of the gas molecules at the given temperature.
Questions you may have include:
- What is the equation for the speed of sound in air?
- How do you calculate the speed of sound in air?
- What is the equation for the speed of sound in any gas?
This lesson will answer those questions.
Useful tool: Metric-English Conversion
Speed in air
Air is a relatively fixed mixture of gases, primarily consisting of Nitrogen, Oxygen, Argon and Carbon Dioxide. It also includes varying amounts of water vapor or humidity.
The speed of sound in air is approximately 343 meters/second, 1130 feet/second or 770 miles per hour at room temperature of 20° C (70° F). This speed is primarily a function of temperature. The only other factor that has any effect on the speed of sound in air is the amount of humidity in the air.
Humidity a slight factor
An increase in the amount of humidity in the air increases the speed only small amount. Since humidity can vary so much, and since the amount of change of speed with an extreme change in humidity is less the 0.5%, the speed of sound in air is usually simply measured in dry air, neglecting the effect of humidity.
Pressure not a factor
Counter to intuition, changes in air pressure have no real effect on the speed of sound. Sound travels slower at higher altitudes because the temperature and relative humidity are lower, not because the air pressure is lower higher altitudes.
Calculating the speed of sound
The speed of sound in dry air in meters per second (m/s) is approximately equal to:
v = 331.4 + 0.6TC m/s
- v = the speed or velocity of sound
- TC is the Celsius temperature.
If TC = 0° C, then v = 331.4 + 0 = 331.4 m/s
If TC = 20° C, then v = 331.4 + 0.6*20 = 331.4 + 12 = 343.4 m/s
This also shows that as the temperature of air goes up, the speed of sound goes up
Speed in any gas
The speed of sound in any gas is a function of temperature, the molecular structure of the gas and its molecular mass. The molecular mass is the atomic weight of the molecule divided by 1000.
Speed in various gases
The speed of sound for various gases at 0° C:
Speed limited by velocity of particles
An interesting characteristic of the speed of sound in a gas is that the speed is a distinct fraction of the average speed or velocity of the molecules or atoms making up the gas.
For example, the speed of sound in air is 0.68 times the speed of the air molecules at a given temperature.
The speed of sound in a gas is a function of its temperature. Air is a mixture of gases and includes water vapor. A simple equation can be used to approximate the speed of sound. A more complex equation takes into account factors and can be used with other gases. The speed of sound in a gas is a specific fraction of the average speed of the gas molecules at the given temperature.
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Resources and references
Speed of Sound - Wikipedia
Sound Speed in Gases - HyperPhysics
Sound Properties and their Perception - High School Physics tutorial
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Speed of Sound in a Gas