Waves
Shock Wave Angle (Mach Cone)
Half-angle of the Mach cone (shock wave) produced by supersonic object.
Variables
θrad
Mach angle
Half-angle of Mach cone
v_soundm/s
Speed of sound
In the medium
vm/s
Object velocity
Supersonic speed
Munitless
Mach number
Must be > 1
Derivation
From geometry: sound wave travels v_sound·t while object travels v·t, forming cone with sin(θ) = v_sound/v.
Your notes
0/5000
Common questions
What is the Shock Wave Angle (Mach Cone) formula?
Shock Wave Angle (Mach Cone) is written sin(θ) = frac{vₛₒᵤₙd}{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) = frac{vₛₒᵤₙd}{v} = 1/M?
In SI units, θ is mach angle, measured in rad; v_sound 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) = frac{vₛₒᵤₙd}{v} = 1/M.