11.6 CHAPTER 11. 2D AND3D WAVEFRONTS
vaircraft× t vsound× t
θ
The angle between the cone that forms and the direction of the plane canbe found from
the right-angle triangle we have drawn into the figure. We know that sin θ =hypotenuseopposite
which in this figure means:
sin θ =
opposite
hypotenuse
sin θ =
vsound× t
vaircraft× t
sin θ =
vsound
vaircraft
In this case we have used sound and aircraft buta more general way of saying this is:
- aircraft = source
- sound = wavefront
We often just write the equation as:
sin θ =
vsound
vaircraft
vaircraftsin θ = vsound
vsourcesin θ = vwavefront
vssin θ = vw
From this equation, wecan see that the faster the source (aircraft) moves, the smaller
the angle of the Mach cone.
Exercise 11 - 2
In this exercise we will determine the Mach Cone Angle for the differentaircraft in the
table mentioned above.To help you get startedwe have calculated theMach Cone
Angle for the Concordewith a speed of sound vsound= 340 m· s−^1.
For the Concorde we know the speed and we know that:
sin θ =
vsound
vaircraft