The speed of sound is the distance traveled per unit of time by a sound wave as it propagates through an elastic medium. It is a fundamental concept in acoustics, fluid dynamics, and many areas of physics. The speed of sound varies depending on the medium through which the sound waves travel and is generally faster in solids than in liquids, and faster in liquids than in gases.

The general formula for the speed of sound is:

\[ v = \sqrt{\frac{K}{\rho}} \]

Where:

- \( v \) is the speed of sound (in meters per second, m/s)
- \( K \) is the bulk modulus of the medium (in Pascals, Pa)
- \( \rho \) is the density of the medium (in kilograms per cubic meter, kg/m³)

For specific mediums, we often use simplified formulas:

- For air: \( v = 331.3 \sqrt{1 + \frac{T}{273.15}} \) m/s
- For water: \( v = 1403 + 4.7T - 0.04T^2 \) m/s
- For steel: \( v = 5920 - 0.3T \) m/s

Where \( T \) is the temperature in degrees Celsius.

Let's calculate the speed of sound in air at 20°C:

- Given:
- Medium: Air
- Temperature (\( T \)) = 20°C

- Apply the formula for speed of sound in air: \[ v = 331.3 \sqrt{1 + \frac{T}{273.15}} \]
- Substitute the known temperature: \[ v = 331.3 \sqrt{1 + \frac{20}{273.15}} \]
- Perform the calculation: \[ v = 331.3 \sqrt{1.0732} \approx 343.2 \text{ m/s} \]

Let's visualize the concept of speed of sound:

This diagram illustrates:

- The sound source (blue circle)
- Sound waves propagating through the medium (green curves)
- The direction and speed of sound propagation (red arrow)
- The calculated speed of sound in air at 20°C

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