The speed of light is approximately Mach 874,635.6.
Understanding Mach Number
The Mach number (M) is a dimensionless quantity representing the ratio of the speed of an object moving through a fluid to the speed of sound in that fluid.
- Mach 1 is defined as the speed of sound itself.
- A speed greater than Mach 1 is considered supersonic.
- A speed significantly less than Mach 1 is subsonic.
The Calculation: Speed of Light in Mach
To determine the Mach equivalent of the speed of light, we compare the speed of light to the speed of sound in a standard medium, typically air at a specific temperature.
Key Values
For this calculation, we use the following widely accepted approximate values:
- Speed of Sound in Air (Mach 1): Approximately 343 meters per second (m/s) in dry air at 20°C (68°F) at sea level. This value can vary with temperature and humidity.
- Reference: NASA Glenn Research Center
- Speed of Light in Atmosphere: Approximately 3 x 10^8 meters per second (m/s), which is the speed of light in a vacuum. The speed of light changes very little when passing through Earth's atmosphere, making this a suitable approximation for practical purposes.
Calculation Breakdown
The Mach number is calculated using the formula:
Mach Number = (Speed of Object) / (Speed of Sound)
For the speed of light:
-
Divide the speed of light by the speed of sound:
300,000,000 m/s ÷ 343 m/s -
Result:
Approximately 874,635.5685... -
Rounded Value:
When rounded to one decimal place, the speed of light is Mach 874,635.6.
Data Summary
| Measurement | Value | Unit |
|---|---|---|
| Speed of Sound (Mach 1) | 343 | m/s |
| Speed of Light | 300,000,000 (3 x 10^8) | m/s |
| Mach Equivalent of Light | ~874,635.6 | Mach |
Implications
This extremely high Mach number underscores the immense difference in scale between the speed of sound, which is perceptible in our daily lives, and the speed of light, which governs the propagation of electromagnetic waves and is the universal speed limit for information and matter. While the Mach scale is primarily used in aerodynamics and for objects moving through air or water, applying it to light illustrates just how incredibly fast light travels relative to sound.
