SME
Compressible Flow · Problem type
Mach angle
Use this for “A jet flies at M = 2. What is the half-angle μ of its Mach cone? What M gives μ = 45°?”
Diagram
The
point
outruns
its
sound:
the
fronts
pile
up
on
a
cone
at
μ
=
sin⁻¹(
1
2
)
=
30°.
Ahead of it, nothing is heard yet.
This is an example. Type your own values to start a new problem.
μ (°)
=
sin⁻¹
1
M
Formulas
μ
=
sin⁻¹(
1
M
)
30
=
sin⁻¹(
1
2
)
Assumptions
•
Sound spreads at speed a in every direction; the source moves at M times a.
•
The fronts meet in a cone only when M > 1; at M = 1 the cone opens flat (μ = 90°).
•
Weak waves only: strong shocks stand at angles larger than μ.
Step-by-step
WE KNOW
M = 2
FIND
Mach angle (μ)
Step 1 · Find Mach angle (μ)
Use μ = sin⁻¹(1 ÷ M)
In
time
t
the
source
moves
M
×
a
×
t
while
the
sound
moves
a
×
t,
so
sin
μ
=
1
M
.
μ
=
sin⁻¹(
1
2
)
μ
=
30°
Check
Put the numbers back in. Both sides should match.
30
=
sin⁻¹(
1
2
)
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.