Why Do People on a Hyperbola Hear a Sonic Boom Simultaneously?

[cjpul]

I found multiple sources that describe the hyperbola of a sonic boom as "A sonic boom shock wave has the shape of a cone, and it intersects the ground in part of a hyperbola. It hits every point on this curve at the same time, so that people in different places along the curve on the ground hear it at the same time. Because the airplane is moving forward, the hyperbolic curve moves forward and eventually the boom can be heard by everyone in its path."

How is it possible that people on the points of the hyperbola hear the sonic boom at exactly the same time? This confuses me considering their distances change from the center. Also, is this assuming that the plane is the center?

Thank you in advance.

 

[HallsofIvy]

I found multiple sources that describe the hyperbola of a sonic boom as "A sonic boom shock wave has the shape of a cone, and it intersects the ground in part of a hyperbola. It hits every point on this curve at the same time, so that people in different places along the curve on the ground hear it at the same time. Because the airplane is moving forward, the hyperbolic curve moves forward and eventually the boom can be heard by everyone in its path."

How is it possible that people on the points of the hyperbola hear the sonic boom at exactly the same time?[/itex] It isn't and the picture you show does not say that.

This confuses me considering their distances change from the center. Also, is this assuming that the plane is the center?

Center of what?

Thank you in advance.

 

[cjpul]

Center of the hyperbola. Also to be clearer, different points on the hyperbola are different distances from the center of the hyperbola.

So how would two people on different points hear the sonic boom at the same time?