Wave Field Effects

When we consider the propagation of a wave form as seen by a sensor, we must consider two cases. The first case known as the Far field occurs when the sensor is of significant distance from the wave source. As the curved wave form travels, it becomes more spread out across the normal of the direction of travel. This effect causes the wave shape to become more planar. The Far Field condition is found at the distance where the wave form becomes a plane wave rather than the curved shape it was omitted as. For the purpose of the linear array, we can define this position by the inequality R > 2d/(wavelength) where R is the radial distance to the source and d is the distance between sensors. For distances that are less than this condition, the effect is observed in the Near Field, where the waveform still retains curvature in its shape. This effect is shown in the animation below. Notice that as the wave travels, the curvature is reduced.

If two sensors reside in the far field distance from the source, the plane wave can be used to calculate the arrival angle based on the time delay between the two intercepting sensors. In our experiment it is necessary to find two unique angles in order to calculate a position. This is accomplished by using the array shape to create a combined near and far field situation. Each microphone in a pair can be distanced in such a way that the far field condition is met, while the array itself is of large enough length to reside in the near field.

This approach allows the array to be subject to curved waveforms while the individual pairs of sensors view a small enough section of the wave form to be considered a plane wave. Assuming that the condition for both situation s is met with the distances, two different angles can be calculated and thus a position can be determined as explained in the A href="calcpos.html">previous section. If the two angles are calculated and found to be equal, then the condition has not been met and the entre array is said to be in the near field. In this case, although a position cannot be determined, the calculated angle still points in the direction of the emitting source. The calculation of the angle based on these principles is explained in detail witinin the section on 'Angle of Arrival'.