Derivation of sin(a) = 1/M. Picture the Mach Cone. Jet flying horizontally to the left. Sound radiates outwards in circles at each moment in time (actually sphere, but circle in 2D drawing on paper). Draw a triangle from the current position of the Jet, right to a previous position of the jet, then down/left as the radius of the circle for how far sound has traveled in that period of time, then your current jet position back to where you are now on the circle, that's the diagonal mach cone line. I hope I haven't lost you yet. This triangle is a right triangle since the mach cone is tangent to the circles of sound expansion. I'll call the mach cone diagonal line the base, the distance sound traveled as the height, and the hypotenuse is the distance the jet traveled. Angle Alpha is angle between the jet line and the mach cone line. So, sin(a) is opposite over hypotenuse, which is distance sound traveled divided by distance jet traveled. distance is velocity*time, so Vsound*T / (Vjet*time). Time cancels so sin(a) = Vsound/Vjet. Vsound/Vjet is an upside down mach number, so 1/M. It's hard to explain a drawing in words, so I hope this made sense. Thanks for watching.
Underrated channel + video. I liked. Would like to know where those formulas come from btw why sin(α) = 1/M ?
Derivation of sin(a) = 1/M. Picture the Mach Cone. Jet flying horizontally to the left. Sound radiates outwards in circles at each moment in time (actually sphere, but circle in 2D drawing on paper). Draw a triangle from the current position of the Jet, right to a previous position of the jet, then down/left as the radius of the circle for how far sound has traveled in that period of time, then your current jet position back to where you are now on the circle, that's the diagonal mach cone line. I hope I haven't lost you yet. This triangle is a right triangle since the mach cone is tangent to the circles of sound expansion. I'll call the mach cone diagonal line the base, the distance sound traveled as the height, and the hypotenuse is the distance the jet traveled. Angle Alpha is angle between the jet line and the mach cone line. So, sin(a) is opposite over hypotenuse, which is distance sound traveled divided by distance jet traveled. distance is velocity*time, so Vsound*T / (Vjet*time). Time cancels so sin(a) = Vsound/Vjet. Vsound/Vjet is an upside down mach number, so 1/M. It's hard to explain a drawing in words, so I hope this made sense. Thanks for watching.
Thank, I had to do a plan to understand what you were saying but I finally get it now. Thanks again!@@BrianBernardEngineering