Shock Wave Angle (Mach Cone)
Half-angle of the Mach cone (shock wave) produced by supersonic object.
Variables
Derivation
From geometry: sound wave travels v_sound·t while object travels v·t, forming cone with sin(θ) = v_sound/v.
Your notes
Check value
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- M = 2 (Mach number)
Result: θ = 0.52359878 rad
Where this formula is listed
- Waves formulas, under Sound Waves, alongside Sound Level (Decibels), Beat Frequency and Sound Intensity Level Addition.
- In the waves list it comes after Mach Number and before Sound Intensity Level Addition.
- Waves formula sheet, one of 37 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Shock Wave Angle (Mach Cone) formula?
Shock Wave Angle (Mach Cone) is written sin(θ) = v_sound/v = 1/M. Half-angle of the Mach cone (shock wave) produced by supersonic object. It belongs to Waves, under Sound Waves.
What are the units in sin(θ) = v_sound/v = 1/M?
In SI units, θ is mach angle, measured in rad; v_s ound is speed of sound, measured in m/s; v is object velocity, measured in m/s; M is mach number (dimensionless).
How is the Shock Wave Angle (Mach Cone) formula derived?
From geometry: sound wave travels v_sound·t while object travels v·t, forming cone with sin(θ) = v_sound/v. The result is sin(θ) = v_sound/v = 1/M.