Speed of Sound Calculator

Understanding Speed of Sound Calculator

The speed of sound in air increases with temperature. At 20°C, it's approximately 343 m/s (1,235 km/h or Mach 1).

How to use this calculator

1. Enter the air temperature in degrees Celsius, \(T\).
2. Use the formula to calculate the speed of sound, \(v\), in meters per second.
3. Check the result to see how temperature changes the speed of sound.
4. Compare different temperatures to understand the trend, warmer air gives a higher speed.

The formula explained

The formula \(v = 331.3\sqrt{1 + \frac{T}{273.15}}\) computes the speed of sound in air from the temperature in Celsius. It gives the speed in meters per second, \(\text{m/s}\).

• v = speed of sound in air, in meters per second
• T = air temperature in degrees Celsius
• 331.3 = reference speed of sound at \(0^\circ\text{C}\), in meters per second
• 273.15 = a temperature constant used in the Celsius to absolute-temperature relationship

Step by step method

1. Start with the temperature \(T\) in degrees Celsius.
2. Substitute \(T\) into \(v = 331.3\sqrt{1 + \frac{T}{273.15}}\).
3. Evaluate the expression inside the square root, then take the square root and multiply by \(331.3\).

Worked example

Problem. Find the speed of sound in air at \(20^\circ\text{C}\).

1. Substitute \(T = 20\) into the formula: \(v = 331.3\sqrt{1 + \frac{20}{273.15}}\).
2. Compute the fraction: \(\frac{20}{273.15} \approx 0.0732\), so \(v = 331.3\sqrt{1.0732}\).
3. Find the square root and multiply: \(\sqrt{1.0732} \approx 1.036\), so \(v \approx 331.3 \times 1.036 \approx 343.1\).

Tips and common mistakes

• Make sure the temperature is in degrees Celsius, not Fahrenheit.
• A higher temperature gives a higher speed of sound, so the result should increase as \(T\) increases.

Frequently asked questions