How does the X-59 acheive quiet supersonic flight?
The X-59 has not yet flown, but according to the designers...


  The ground noise is expected to be around 60 dB(A), about 1/1000 as
  loud as current supersonic aircraft. This is achieved by using a long,
  narrow airframe and canards to keep the shock waves from coalescing.
  It should create a 75 Perceived Level decibel (PLdB) thump on ground,
  as loud as closing a car door, compared with 105-110 PLdB for the
  Concorde. The central engine has a top-mounted intake for low boom,
  but inlet flow distortion due to vortices is a concern.


Source: Wikipedia

Additional information on this NASA project is available here.