# What happens to a supersonic shockwave if the object stops?

Just wanted to ask what would happen to a supersonic shockwave if the object creating it suddenly stopped, for example a bullet. In the image attached I would expect to hear the supersonic crack of the bullet if I was standing at any of the red circle locations, as the bullet would be passing me as the listener, however would I hear that supersonic crack if I were to stand at any of the green circle locations? The bullet and the shockwave around it have already stopped travelling and therefore would not pass by me. But would the shockwave travelling behind it still be audible after the bullet stops or would it dissipate into the earth out outwards from where the bullet hit ?

Many thanks for any help on this.

...however would I hear that supersonic crack if I were to stand at any of the green circle locations?

It depends on how far away from the target you are located. The shock itself would immediately start to damp and reduce to an ordinary sound wave after its piston (i.e., the bullet here) stopped driving the shock. Without the piston, shocks in collisional media mass load very quickly and die out, i.e., it becomes weaker which corresponds to a decreased Mach number (e.g., see relation to density at https://physics.stackexchange.com/a/349724/59023). The rate at which it dies is related to the energy dissipation rates it experiences as it propagates.

Once the piston is gone, you could approximate the remaining shock as a blast wave. So after the piston stops in the target, the speed will decrease proportional to $U_{shn}\left(t\right) \propto \sqrt{\tfrac{E_{o}}{\rho_{up}}} \ R\left(t\right)^{-3/2}$, where $E_{o}$ is related to the initial energy released (e.g., the energy of the bullet), $\rho_{up}$ would be the mass density of the ambient air, $t$ is the time from initiation, and $R\left(t\right) \propto \left( \tfrac{E_{o}}{\rho_{up}} \right)^{1/5} \ t^{2/5}$ is the distance from the target.

This is a crude approximation, but it would suffice for what you asking.

But would the shockwave travelling behind it still be audible after the bullet stops or would it dissipate into the earth out outwards from where the bullet hit?

As an aside, it is rare to hear the actual sonic boom of a bullet because the sound produced by the explosion of the gun powder that accelerates the round is typically so much louder. Generally the bullet needs to pass very close to you in order to hear a the distinct crack of the sonic boom.

• Hi honeste_vivere many thanks for taking the time to reply and huge thanks for the detailed response. Really appreciate it. Nov 18 '17 at 12:00