Superposition. Fourier Series Constructive Interference of a pulse.

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Presentation transcript:

Superposition

Fourier Series

Constructive Interference of a pulse

Destructive Interference of a pulse

Constructive Interference of Harmonic Waves

Destructive Interference of Harmonic Waves

2 Dimensional Example

Single Hydrophone Display 1 “omni-directional” hydrophone processor

Two Hydrophones Beam Former 1 2 hydrophonesprocessor Display Why not ???

Incident Wave Beam Former 1 2 xx d  Display

Identities

Power Output from the Processor

Beam Pattern Function Trig identity

Example =.5 d  =0 

Maximum Power Directions  =0 

Null Angles  =0 

Beam Width The beamwidth of a beam is the angular displacement between the angles where the beam pattern function, b(  ), is greater than dB down points The beamwidth is important because it is proportional to the bearing accuracy of the specific beam.  =0 

3-d Beam Pattern

Effect of Increasing Frequency

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