Speed of Sound to Mach Number Converter
Convert the speed of sound in air (at a given temperature) to the **Mach number**. The Mach number is the ratio of the object’s speed to the speed of sound in the surrounding medium.
Instructions:
- Enter the **speed in meters per second (m/s)**.
- Enter the **air temperature in Celsius (°C)**.
- Click “Convert to Mach Number” to calculate the **Mach number**.
When discussing speed, particularly in aerodynamics or physics, the Mach number is a key concept. It is a ratio that compares an object’s speed to the speed of sound in the medium it’s traveling through. Converting the speed of sound to Mach number helps understand the relative speed of an object—whether it’s supersonic, subsonic, or hypersonic.
In this guide, we’ll cover how to convert the speed of sound to the Mach number and vice versa.
What is the Mach Number?
The Mach number (M) is a dimensionless value representing the ratio of an object’s speed to the speed of sound in the surrounding medium. The formula for the Mach number is:
Mach number (M) = Speed of the object (v) / Speed of sound in the medium (a)
Where:
- v = Speed of the object
- a = Speed of sound in the medium
Speed of Sound (a)
The speed of sound depends on the medium and its temperature. For example, in air at sea level, the speed of sound is approximately:
- At 20°C (68°F): 343 meters per second (m/s)
- At 0°C (32°F): 331 m/s
- At 15°C (59°F): 340 m/s
For other mediums:
- In water (at 20°C): approximately 1,480 m/s
- In steel: around 5,100 m/s
How to Convert Speed to Mach Number
To convert a given speed to a Mach number, divide the object’s speed by the speed of sound in the medium.
Formula: Mach number (M) = Speed of the object (v) / Speed of sound (a)
Example:
If an aircraft is traveling at 1,500 m/s in air at 20°C, the Mach number would be:
M = 1,500 m/s / 343 m/s ≈ 4.38
So, the aircraft is traveling at Mach 4.38.
Mach Number Reference Chart
Here’s a reference table showing common speeds and their corresponding Mach numbers using the speed of sound in air at 20°C (343 m/s) for the conversion.
| Speed (m/s) | Mach Number | Description |
|---|---|---|
| 343 | Mach 1 | Speed of sound (air) |
| 500 | Mach 1.46 | Subsonic |
| 1,000 | Mach 2.92 | Transonic |
| 1,500 | Mach 4.38 | Supersonic |
| 2,000 | Mach 5.82 | Supersonic |
| 3,000 | Mach 8.75 | Hypersonic |
| 5,000 | Mach 14.6 | Hypersonic |
- Mach 1 = Speed of sound
- Mach 2 = Twice the speed of sound
- Mach 5 = Five times the speed of sound (hypersonic speed)
Converting from Mach Number to Speed
To convert from Mach number to the speed of the object, use this formula:
Speed of the object (v) = Mach number (M) × Speed of sound (a)
Example:
To find the speed of an object traveling at Mach 3 in air at 20°C:
v = 3 × 343 m/s = 1,029 m/s
So, the object is traveling at 1,029 m/s.
FAQ: Common Questions About Speed of Sound and Mach Number
Q: What happens when an object reaches Mach 1?
A: When an object reaches Mach 1, it is moving at the speed of sound. This is often called the sound barrier, and breaking it can cause a sonic boom.
Q: Is the Mach number the same at all altitudes?
A: No, the speed of sound changes with altitude. The air is cooler at higher altitudes, so the speed of sound decreases, which means the same speed will correspond to a different Mach number at higher altitudes.
Q: Can the Mach number exceed 1?
A: Yes! A Mach number greater than 1 means the object is traveling at supersonic speeds. Speeds of Mach 5 and above are considered hypersonic.
Q: How does temperature affect the speed of sound?
A: The speed of sound increases with temperature. For example:
- At 0°C, the speed of sound is 331 m/s.
- At 20°C, it’s 343 m/s.
- At 40°C, it’s about 349 m/s.
Why Understanding the Speed of Sound and Mach Number Matters
Knowing how to convert between speed of sound and Mach number is crucial for many fields, including:
- Aerospace Engineering: For designing supersonic and hypersonic aircraft.
- Meteorology: To study shockwaves, sonic booms, and weather phenomena like thunder.
- Physics: For understanding wave propagation in various media.
Conclusion
Understanding the Mach number and its relationship to the speed of sound is key when dealing with high-speed motion. Whether you’re working in aviation, space exploration, or just curious about how speed is measured at different levels, this conversion can provide valuable insights. Use the formulas and reference charts above to quickly convert speeds and gain a better understanding of aerodynamics and acoustics.