Mach Cone and Sonic Boom
Build a Mach cone from moving wavefronts and measure its half-angle.
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Mach Cone and Sonic Boom
In still uniform air of sound speed 343 m/s, a source travels at a certain Mach number (M). When M > 1, the emitted circular wavefront sections form a Mach-cone envelope. The half-angle from the forward velocity axis obeys sin(μ) = 1/M.
Worked Example
Consider a source traveling at Mach 2 for an elapsed time of 1 second.
- Source travel distance: 2 * 343 * 1 = 686 m.
- Wave radius for the earliest wave: 343 * 1 = 343 m.
- Mach angle: arcsin(1/2) = 30°.
We expect the simulation to yield exactly 686 for source travel, 343 for wave radius, and 30 for the angle.
Experiment
You can interact with the Mach Cone visualization by selecting different Mach numbers and elapsed times.
- Select Mach number = 0.5. Observe that the source remains inside the wavefronts and no Mach cone is formed.
- Select Mach number = 1. The sonic limit is reached, forming a vertical limiting front (90°).
- Select Mach number = 2. A proper Mach cone forms at an angle of 30°.
Try it yourself here: Mach Cone and Sonic Boom Interactive Module.
Limitations
This module illustrates geometric acoustics based on points and spherical wavefronts. It does not model shock-pressure CFD, density variations, or three-dimensional sound intensity decay. The boom is experienced on the moving shock, not only at the instant a source accelerates through Mach 1.
References
This reference provides an interactive applet and mathematical derivations for the Mach angle and supersonic flow, helping to understand the relationship between Mach number and the cone geometry.
Experience it interactively
Adjust parameters, observe in real time, and build deep intuition with Riano’s interactive Mach Cone and Sonic Boom module.
Try Mach Cone and Sonic Boom on Riano →