fizzy said:
So shock waves are not "sound waves" and travel faster than the "speed of sound". So when we hear the crack of an F15 fly past we should remember that we are not hearing a sound ! The roar that follows is sound but not the boom.
Shock waves are a degenerate form of a sound wave (or pressure wave, same thing). When a pressure wave moves through air, it subtly changes the properties of the gas, and in particular, it raises the temperature slightly. That slight increase in temperature means that there is a slight increase in the speed of sound in that region just behind a pressure wave. For most waves, the amplitude is not large enough for this to make any real difference; the wave will dissipate long before any piece of the downstream wave catches up to the peak. However, if the wave is strong enough, then it can "break" when the wave "catches up with itself". If you plotted the pressure over time, the wave front would be vertical at that point, and if the wave continued to "catch itself" it would become a multi-valued function, which can't physically happen. When the wave breaks, it does so by forming a shock, which have similar but different properties than the weak waves that never break. You can hear them both under the right circumstances, so it is still "sound". The reference I linked earlier,
Elements of Gasdynamics, has a pretty good discussion of this, as does
Linear and Nonlinear Waves that I linked even earlier in the discussion.
fizzy said:
So the pointed object does not push air forwards, does not produce the same pressure and velocity gradient and thus no shock wave.
No, it still produces a shock wave. It produces an attached oblique shock wave, which is what creates a Mach cone. If the cone angle is too steep or the tip is blunt, then you get a detached bow shock that exists slightly in front of the tip (how far depends on a lot of factors) and that shock eventually bends around and forms a Mach cone just like a normal oblique shock would.
fizzy said:
Since it is a variable quantity there is no useful meaning to THE speed of sound. It can only be used in that way if you use it as a shorthand for the speed of sound in standard conditions: dry air STP etc.
Just because something is variable doesn't mean it isn't clearly definable quantity. The speed of sound is the speed at which pressure waves move through a medium at a given set of conditions.
fizzy said:
None of this contradicts my description of the shock wave moving faster than the regionally local "speed of sound" because the speed of propagation is increased by the pressure in front of the aircraft.
The shock is moving faster than the speed of sound in the medium
into which it is propagating, which is completely fine. However, the shock wave is still moving less than the speed of sound in the medium
through which it is propagating. That is the important difference.
fizzy said:
So if we are to reserve "speed of sound" for small amplitude pressure waves I should substitute the speed of propagation of the pressure wave but the essense of what I said is correct.
There is no difference there. Acoustic waves are pressure waves, and their properties obey the same rules regardless of amplitude until they break.
fizzy said:
You cannot say that air which is not in contact with the metal nose is being "pushed along" and therefore some part of its speed does not "count". Clearly all the air except the static thin film which is in contact with the metal is being accelerated by the air pressure behind it. It is a pressure wave and its speed is the speed of propagation of that pressure wave. No handwaving, word games or adjustments required.
Of course I can, because that is exactly what is happening. Because the air just in front of a blunt tip is subsonic relative to the plane, the influence of the plane can be felt for some distance upstream of the plane. However, since the plane is moving supersonic relative to the air it is moving into, there must be a shockwave that forms because the plane and the thin layer of air it pushes along with it will reach the undisturbed medium faster than pressure waves can propagate out further in front.