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Explanation of the speed of sound waves in a gas - Succeed in Physical Science. Also refer to physics, air, temperature, nitrogen, oxygen, water vapor, argon, carbon dioxide, pressure, equation, meters per second, Celsius, Fahrenheit, molecular mass, average velocity, Ron Kurtus, 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. There is a mini-quiz near the end of the lesson.

Useful tools: Metric-English Conversion | Scientific Calculator.

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 + 0.6T_C m/s

where

• v = the speed or velocity of sound
• T_C is the Celsius temperature.

Examples

If T_C = 0° C, then v = 331.4 + 0 = 331.4 m/s

If T_C = 20° C, then v = 331.4 + 0.6*20 = 331.4 + 12 = 343.4 m/s

This also shows how as the temperture 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.

Summary

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.

Answers to Readers' Questions

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Resources

The following resources provide information on this subject:

Websites

Speed of Sound - Wikipedia

Sound Speed in Gases - HyperPhysics

Sound Properties and their Perception - High School Physics tutorial

Physical Science Resources

Books

Top-rated books on Sound

Miscellaneous

Mini-quiz to check your understanding

1. What happens to the speed of sound in air on a humid day?

2. What happens to the velocity of sound as the temperature increases?

3. If air molecules are traveling at 500 meters per second, what is the speed of sound?

If you got all three correct, you are on your way to becoming a Champion in Physical Science. If you had problems, you had better look over the material again.

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Speed of Sound in a Gas