How to calculate the speed of sound
Sound waves travel through gases and liquids as longitudinal waves (the medium vibrates in the propagation direction). The speed at which these waves travel through different mediums is called the speed of sound and is a property of the medium.
To calculate the speed of sound in, let's say, air, you need to divide the distance traveled by the wave by the time it took to reach that distance.
Here's one simple experiment to calculate the speed of sound outdoors:
- Get a timer and find an open area where you won't be interrupted by other noises.
- Ask a friend to stay ~100 m away from you.
- Ask your friend to clap their hands up in the sky so you can clearly see when both palms touch and start the timer.
- Stop the timer when you hear the clapping sound.
- Divide 100 m by the time (in seconds) you registered with your timer. If you were extremely precise, the result is the speed of sound for the air conditions where you took the measurement.
You can repeat this experiment multiple times and take the average to get a more accurate value.
Speed of sound in air formula
We can assume the air to be an ideal gas for simplification purposes. The speed of sound formula for an ideal gas is:
- - the molar gas constant, approximately 8.314,5 J · mol⁻¹·K⁻¹.
- - the adiabatic index, approximately 1.4 for air.
- - the temperature, in kelvins.
- - the molar mass of the gas. For dry air is about 0.0289645 kg/mol.
If we replace the parameters in the speed of sound formula with the values for air, we get:
where again is the temperature in kelvins. Keep in mind this value might change for moist air. We recommend reading the article about relative humidity in the if you want to know more.
Speed of sound in water
The speed of sound in water is considered to be 1482 m/s at 20°C. This means sound travels almost five times faster in water than in air.
This tool can also output the speed of sound in water at any temperature. While there's no simple formula for it, we can look at ato find it.