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So from what I know sonic boom occurs when sound from large sections of the trajectory arrive simultaneously so a hyper-sonic spacecraft travels over a flat plain on Earth what shape will the loci of points which experience the shock-wave at a given moment make on the surface?

I was thinking maybe a N shape because there is a rise in pressure at the nose, decreasing steadily to a negative pressure at the tail, followed by a sudden return to normal pressure after the object passes.and this "over-pressure profile" is known as an N-wave because of its shape. The "boom" is experienced when there is a sudden change in pressure, so the N-wave causes two booms, one when the initial pressure rise from the nose hits, and another when the tail passes and the pressure suddenly returns to normal.

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  • $\begingroup$ Your question is confusing for two reasons. First, you need to read up on what really causes a sonic boom. Second, it isn't clear whether you're talking about the pressure over time at a single point on the surface, or the pressure across the surface at a single moment in time. $\endgroup$ – Daniel Griscom Nov 4 '15 at 23:58
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what shape will the loci of points which experience the shock-wave at a given moment make on the surface?

The answer is given in the attached pictures. The conical shock wave generated by the supersonic plane continues to spread out until it hits the ground. The locum will be the intersection between a cone (2 cones, ones inside the other, because both the front and the back of the plane generate strong shock waves) and the surface of the earth.

Shock wave hitting the surface if the earth

Source

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  • $\begingroup$ This is an example of a conic section. It will be a hyperbola if the plane flies up; a parabola in the particular case where the plane flies exactly horizontally; and an ellipse (!) if the plane is climbing. $\endgroup$ – Floris Nov 5 '15 at 1:24

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