Wave Interaction or Interference

Wave propagation has been discussed so far as if a single sinusoidal wave was propagating through the material. However, the sound that emanates from an ultrasonic transducer or the EM waves that radiate from an antenna do not originate from a single point, but instead originates from many points. This results in a field with many waves interacting or interfering with each other.

When waves interact, they superimpose on each other, and the amplitude of the sound pressure or particle displacement at any point of interaction is the sum of the amplitudes of the two individual waves. First, let's consider two identical waves that originate from the same point. When they are in phase (so that the peaks and valleys of one are exactly aligned with those of the other), they combine to double the displacement of either wave acting alone. This is the case on the left and this is called constructive interference. When they are completely out of phase (so that the peaks of one wave are exactly aligned with the valleys of the other wave), they combine to cancel each other out. This is the case in the middle and this is a case of destructive interference. When the two waves are not completely in phase or out of phase, the resulting wave is the sum of the wave amplitudes for all points along the wave. This is the case on the right and in this case there is both constructive and destructive interference. 

When the origins of the two interacting waves are not the same, it is a little harder to picture the wave interaction, but the principles are the same. Up until now, we have primarily looked at waves in the form of a 2D plot of wave amplitude versus wave position. However, anyone that has dropped something in a pool of water can picture the waves radiating out from the source with a circular wave front. If two objects are dropped a short distance apart into the pool of water, their waves will radiate out from their sources and interact with each other. At every point where the waves interact, the amplitude of the particle displacement is the combined sum of the amplitudes of the particle displacement of the individual waves.

With an ultrasonic transducer or an antenna, the waves propagate out from the transducer face with a circular wave front. If it were possible to get the waves to propagate out from a single point on the transducer face, the field would appear as shown in the upper image to the right. Consider the light areas to be areas of rarefaction and the dark areas to be areas of compression.

However, as stated previously, waves originate from multiple points along the face of the transducer or antenna. The lower image to the right shows what the field would look like if the waves originated from just two points. It can be seen that where the waves interact, there are areas of constructive and destructive interference. The points of constructive interference are often referred to as nodes. Of course, there are more than two points of origin along the face of a transducer or antenna. The image below shows five points of wave origination. It can be seen that near the face of the transducer, there are extensive fluctuations or nodes and the field is very uneven. In ultrasonic testing and in antenna theory, this in known as the near field (near zone) or Fresnel zone. The field is more uniform away from the transducer in the far field, or Fraunhofer zone, where the beam spreads out in a pattern originating from the center of the transducer/antenna. It should be noted that even in the far field, it is not a uniform wave front. However, at some distance from the face of the transducer and central to the face of the transducer, a uniform and intense wave field develops.

In the image to the left, multiple points of sound origination along the face of the transducer/antenna.

The curvature and the area over which the wave is being generated, the speed that the waves travel within a material and the frequency of the wave all affect the sound field. Use the Java applet below to experiment with these variables and see how the sound field is affected.