Speed of Sound and Mach Number
Calculator and formulas for calculating the speed of sound and Mach number
Speed of Sound & Mach Number Calculator
Sound propagation and Mach number
Calculates the speed of sound (c) as a function of temperature and the resulting Mach number (Ma) for a given velocity.
Example Calculation
Example: Supersonic aircraft at 20°C
Problem:
A supersonic aircraft flies at 1,200 km/h at an air temperature of 20°C. What is the Mach number?
Given:
- Temperature T = 20°C
- Flight velocity v = 1,200 km/h
- Find: Speed of sound c and Mach number Ma
Solution:
1. Calculate speed of sound:
2. Convert velocity:
3. Calculate Mach number:
Mach numbers in aviation
Temperature dependency
Important: The speed of sound depends strongly on temperature. At colder temperatures (e.g. at high altitude) it is lower, which increases the Mach number at the same velocity.
Formulas for speed of sound and Mach number
The speed of sound in air depends mainly on temperature. The Mach number is the ratio of flow velocity to the speed of sound.
Speed of sound in air
Calculation of speed of sound at given temperature in °C.
T = Temperature [°C]
Mach number
Ratio of flow velocity to speed of sound.
v = Flow velocity [m/s]
c = Speed of sound [m/s]
Conversion km/h ↔ m/s
Conversion between velocity units.
Temperature in the atmosphere
Approximation formula for temperature as a function of altitude.
Classification by Mach numbers
Transonic: 0.8 < Ma < 1.2
Hypersonic: Ma > 5
Fighter jet: Ma ≈ 1.5-2.5
Space Shuttle: Ma ≈ 25
Detailed description of speed of sound and Mach number
Physical Fundamentals
The speed of sound describes the propagation speed of sound waves in a medium. In air, it depends mainly on temperature, as warmer air accelerates molecular motion and thus sound propagation.
The Mach number is a dimensionless ratio and describes how fast an object moves relative to the speed of sound.
Usage Instructions
Enter the air temperature and the velocity of the object. The calculator automatically computes the speed of sound and the resulting Mach number.
Application Areas
Aviation
Aircraft design, performance calculation, aerodynamics. Critical for supersonic aircraft and engine design.
Aerospace
Re-entry of spacecraft, hypersonic velocities. Calculation of heat shield requirements.
Meteorology
Sound propagation in the atmosphere, weather radar systems. Foundation for acoustic measurement methods.
Velocity ranges in aviation
The classification of flight velocities is based on the Mach number and is crucial for aircraft design:
Subsonic (Ma < 0.8)
Commercial aircraft, propeller aircraft
Example: Boeing 737 (Ma ≈ 0.78)
Transonic (0.8-1.2)
Critical range, mixed flow
Example: Modern jets during climb
Supersonic (1.2-5)
Fighter jets, supersonic aircraft
Example: F-16 (Ma ≈ 2.0)
Hypersonic (Ma > 5)
Spacecraft, experimental aircraft
Example: Space Shuttle (Ma ≈ 25)
Note: The speed of sound varies with altitude and temperature. At 11 km altitude (cruising altitude) it is only about 295 m/s instead of 343 m/s at sea level.
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