Pressure Field Due to a Moving Source

• Consider a point source emanating infinitesimal pressure disturbances in a still fluid, in which the speed of sound is "a". If the point disturbance, is stationary then the wave fronts are concentric spheres. As shown in Fig. 39.2(a), wave fronts are present at intervals of Δt .
  
  
• Now suppose that source moves to the left at speed U < a. Figure 39.2(b) shows four locations of the source, 1 to 4, at equal intervals of time , with point 4 being the current location of the source.
  
  
• At point 1, the source emanated a wave which has spherically expanded to a radius in an interval of time 3Δt . During this time the source has moved to the location 4 at a distance of 3uΔt from point 1. The figure also shows the locations of the wave fronts emitted while the source was at points 2 and 3, respectively.
  
  
• When the source speed is supersonic U > a (Fig. 39.2(c)), the point source is ahead of the disturbance and an observer in the downstream location is unaware of the approaching source. The disturbance emitted at different

Fig 39.2 Wave fronts emitted from a point source in a still fluid when the source speed is
(a) U = 0 (still Source)    (b) U < a (Subsonic)   (c) U > a (Supersonic)

see animated view here

points of time are enveloped by an imaginary conical surface known as "Mach Cone". The half angle of the cone , is known as Mach angle and given by

• Since the disturbances are confined to the cone, the area within the cone is known as zone of action and the area outside the cone is zone of silence .
  

  An observer does not feel the effects of the moving source till the Mach Cone covers his position.