1. Constructive and Destructive Interference Beam Forming and Beam Steering

2. If vector A and vector B are pointing in the same direction the magnitude of vector A and the magnitude of vector B sum to create a greater magnitude vector C travelling in the same direction. Vector Math If vector A and vector B are pointing in the opposite direction the magnitude of vector A and the magnitude of vector B cancel to create no vector C.

3. In the real world vectors do not always point in the same direction. To find the magnitude in a certain direction vectors can be broken down into x and y components and then summed as in the previous example. Vector Math

4. Electromagnetic Waves

5. Electromagnetic waves are transverse waves The magnetic (H) field vector is perpendicular to the direction of motion. The electric (E) field vector is perpendicular to the direction of motion The magnetic field, electric field and direction of motion vectors are all 90 degrees apart. A cancelling signal would be identical to the target electromagnetic wave (type), be 180 degrees out of phase (both H and E), and be of equal or greater intensity (ie magnitude, amplitude). The longitudinal motion of the wave is not important in cancelling the target wave.

6. Acoustic Waves Acoustic waves are pressure waves, which consists of a compression phase and a rarefaction phase. A noise-cancellation speaker emits a sound wave with the same amplitude but with inverted phase (also known as anti-phase) to the original sound. The waves combine to cancel each other out. A noise-cancellation speaker may be co-located with the sound source to be attenuated. In this case it must have the same audio power level as the source of the unwanted sound. Alternatively, the transducer emitting the cancellation signal may be located at the location where sound attenuation is wanted (e.g. the user's ear). This requires a much lower power level for cancellation but is effective only for a single user.

7. Acoustic Waves

8. What is a Pressure Wave? Since a sound wave consists of a repeating pattern of high-pressure and low-pressure regions moving through a medium, it is sometimes referred to as a pressure wave. If a detector, whether it is the human ear or a man-made instrument, were used to detect a sound wave, it would detect fluctuations in pressure as the sound wave impinges upon the detecting device. At one instant in time, the detector would detect a high pressure; this would correspond to the arrival of a compression at the detector site. At the next instant in time, the detector might detect normal pressure. And then finally a low pressure would be detected, corresponding to the arrival of a rarefaction at the detector site. The fluctuations in pressure as detected by the detector occur at periodic and regular time intervals. In fact, a plot of pressure versus time would appear as a sine curve. The peak points of the sine curve correspond to compressions; the low points correspond to rarefactions; and the "zero points" correspond to the pressure that the air would have if there were no disturbance moving through it. The diagram below depicts the correspondence between the longitudinal nature of a sound wave in air and the pressure-time fluctuations that it creates at a fixed detector location.

9. Acoustic Waves

10. Sound Waves and the Eardrum When a pressure wave reaches the ear, a series of high and low pressure regions impinge upon the eardrum. The arrival of a compression or high pressure region pushes the eardrum inward; the arrival of a low pressure regions serves to pull the eardrum outward. The continuous arrival of high and low pressure regions sets the eardrum into vibrational motion.

11. Electromagnetic Wave Constructive Interference Waves add in intensity (ie amplitude or magnitude) when their peaks & trough sync (ie of the same type, frequency and phase)

12. Example Video of Constructive Interference

13. Acoustic and electromagnetic waves contain the most energy when first emitted from the source. While in transit the energy of the wave decays exponentially as the wave travels. In the figure, the direction of motion m is North. m=4 m=3 m=2 m=1 Wave Energy MinMax

14. The waves from these routers have already travelled a distance from the source and presently each have magnitude 2. Wave Energy Example AB

15. The waves meet at a point in space (a), are of the same type, frequency and are in phase, therefore where the waves meet, the energies of the two waves will sum. Wave Energy Example a AB

16. The resultant wave is a combination of the two waves A and B. Note the resultant is greater in magnitude than either A or B and moves along a new Northerly path. Wave Energy Example A C B

17. A B D F G C=A+B E=C+D 1) The red and green vectors A & B sum to create the resultant vector C. 2) The burgundy and blue vectors C & D sum to create the resultant vector E. This is an example of wave superposition or constructive interference. Each resultant vector carries more energy than it’s constituents. 3) The purple and orange vectors (not shown) F & G sum to create an equal and opposite vector to E. This is an example of destructive interference. The two vectors of equal magnitude and in opposite directions cancel.

18. Wave Energy Example Beam Forming & Beam Steering When displayed graphically the energy in transit can be visualized as a beam of energy steering through free space.

19. Appendix A - Advantages of Directional Antennas Over Omnidirectional

20. Acoustic (sound) and electromagnetic (wireless) waves can be sent from one location to another using air as a medium. In many applications it’s desirable for the emitter to direct the waves. When waves are directed a gain is realized because the same amount of energy is routed into a smaller square area intensifying the emission. An example of this phenomenon would be a laser beam, ordinary light compressed into a pencil beam. Acoustic and electromagnetic waves contain the most energy when first emitted from the source. While in transit the energy of the wave decays exponentially (for more on this see far field). Waves are represented as vectors because they have an intensity and a direction. When illustrating a vector an arrow shows the intensity (length of the arrow) and the direction. Advantages of Directional Antennas Over Omnidirectional

21. Appendix B – Other Integrated Wave Energy Technologies

22. Vehicular Ad-hoc Networking Beam Forming & Beam Steering When displayed graphically the energy in transit can be visualized as a beam of energy steering through free space.