Superposition

1
Superposition
2
Fourier Series
3
Constructive Interference of a pulse
4
Destructive Interference of a pulse
5
Constructive Interference of Harmonic Waves
6
Destructive Interference of Harmonic Waves
7
2 Dimensional Example
8
Single Hydrophone
Display
1
hydrophone
processor
omni-directional
9
Two Hydrophones
Beam Former
1
Display
2
hydrophones
processor
Why not
???
10
Incident Wave
Beam Former
Display
11
Identities
12
Power Output from the Processor
13
Beam Pattern Function
Trig identity
14
Example l .5 d
15
Maximum Power Directions
16
Null Angles
17
Beam Width

• The beamwidth of a beam is the angular
  displacement between the angles where the beam
  pattern function, b(?), is greater than 0.5.
• 3 dB down points
• The beamwidth is important because it is
  proportional to the bearing accuracy of the
  specific beam.

18
3-d Beam Pattern
19
Effect of Increasing Frequency