Wave-Wave Interactions: Interference of Waves

Waves can combine with other waves to form new waves. When two different waves occur in the same region, the net wave is simply the sum of the displacements of each wave. Combining two or more waves together to form a new wave is called interference. This is called superposition, which is commonly used whan adding vectors at a particular point in space, such as determining the net electric field at a poinjt in space that is generated by two or more electric charges. Like vectors, one does not simply add the amplitudes of waves to get the net waves. One must add the displacments, which can be either posiitive or negative, which can lead to cancellation of the waves (destructive interference) when one displacement is positive and the other negative, or if the amplitudes have the same sign, the waves reinforce each other and the result is constructive interference. Depending on the frequencies, amplitudes, phases, direction of travel, and polarization of the waves that are being added, the resulting wave can look very different. We will investigate how waves combine to form new waves over the next several pages. We will see that two traveling sine waves can combine to form waves that do not look at all like sine waves. Sometimes, the two traveling sine waves can combine to form a sine wave that does not travel.

Experiment with this simulation to develop a more thorough understanding of the interference of two waves travelling in the same direction. Set the amplitude and wavenumber of the travelling waves depicted in the top two graphs (blue and green) below, and observe the sum of the two waves in the bottom graph (red) by pressing the CLAW icon (upper left part of simulation). What happens when the wavlengths are the same? Change the phase constant of the green wave to shift it with respect to the blue wave. What happens when the waves are shifted from each other?

Use the above simulation to answer the following questions?