PhysicsLAB Resource Lesson
Barrier Waves, Bow Waves, and Shock Waves

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When the source moves at a speed equal to the speed of the wave, a barrier wave is produced in front of the source as each successive wave front piles on top of the previous one. This regions of constructive interference pattern is a physical reality that must be overcome if the source is to move any faster. 
Boats, after they break through the barrier wave that is produced when their speeds equal the speed of the water waves in that region, start trailing a two-dimensional bow wave. Down the center of the bow wave is a region of destructive interference while the edges, or wake, are regions of high amplitude constructive interference. As a general rule, the speed of a water wave is principally determined by the water's depth and its temperature.
When planes fly through the "sound barrier," they are doing more than just traveling in excess of 340 m/sec. They have traveled also through a region of high amplitude constructive interference which, for sound waves, is a region of high compression followed by a region of low rarefaction. The pressure differential is tremendous. After breaking through the barrier wave, the plane then trails a three-dimensional bow wave, or a shock cone, and is said to be traveling supersonic. The width of the bow wave or shock cone depends on the speed of the source; the faster the source travels, the narrower the wave becomes.

Use this physlet animation by Wolfgang Christian at Davidson College to watch the wave patterns as the red particle travels faster and faster.
Doppler Effect
Barrier Wave
Bow Wave (2-D)
Shock Wave (3-D)
a stationary wave source a wave source moving to the right at a speed less than the wave speed a wave source moving to the right at a speed equal to the wave speed wave source moving to the right at a speed in excess of the wave speed
When a shock wave, trailing a supersonic plane, passes through your position, you heard a sonic boom. It is actually a "double boom." When the leading edge of the cone passes, it raises equilibrium pressure rapidly upwards (compression), followed by a rapid drop in pressure (rarefaction), followed by a return to equilibrium. We hear a sonic boom whenever the Shuttle's glide path passes over Daytona for its landing at the Cape.
To determine the "Mach" number for a supersonic plane you compare the ratio of the plane's radius to the ratio of the sound's radius. This NextTime question will illustrate the technique. You can practice determining Mach numbers on this worksheet.

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