Everything Science Grade 12

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