Speed of Sound
Local speed of sound (kt) as a function of absolute air temperature (Kelvin).
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Example
At 288 K (15°C): a ≈ 661 kt
How it works
The speed of sound in air is mainly set by how quickly pressure disturbances travel through the gas, which depends on the air temperature. Warmer air molecules move faster, so sound waves propagate faster; cooler air gives a lower speed. This formula is a practical aviation approximation for dry air near standard atmospheric conditions, with the square-root relationship coming from the thermodynamics of gases.
When to use it
Use this when you need an approximate local speed of sound for flight performance, Mach number calculations, or checking whether an aircraft is near transonic speeds. It is especially useful in aviation problems where temperature is known in Kelvin and speed of sound is needed in knots.
Worked example, step by step
Find the speed of sound at T = 250 K. Step 1: Write the formula: a = 38.94√T Step 2: Substitute the temperature: a = 38.94√250 Step 3: Calculate the square root: √250 ≈ 15.81 Step 4: Multiply: a ≈ 38.94 × 15.81 Step 5: Compute the result: a ≈ 615.6 kt Final answer: the speed of sound is about 616 kt.
Common mistakes to avoid
- Using Celsius instead of Kelvin, which gives a wrong result
- Treating the formula as exact for all atmospheric conditions, instead of an approximation for typical air
- Forgetting that the output is in knots, not m/s or km/h
Did You Know?
The speed of sound depends only on air temperature, not pressure — it's slower in the frigid stratosphere.
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