Question Video: Identifying Waveforms That Make up Incoherent Light Physics

The diagram represents the resultant waveform of the waves emitted from an incandescent light source. Which of the following diagrams most correctly represents a group of the waves emitted from the incandescent light source? [A] Diagram I [B] Diagram II

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Video Transcript

The diagram represents the resultant waveform of the waves emitted from an incandescent light source. Which of the following diagrams most correctly represents a group of the waves emitted from the incandescent light source?

In this diagram, then, this red line at the top is the resultant waveform. We could think of this as the final or sum wave form after a series of waveforms are all combined together. The question is, which of these two sets of waveforms, set number one or set number two, is most likely to represent a group of the waves that could result in this final waveform?

To answer this question, we can recall a bit about wave interference. Waves, we know, can interfere constructively. This is where peaks and troughs align so that the resultant wave has a greater overall amplitude. And they can also interfere destructively. This is where the peak and trough of one wave line up with the trough and peak, respectively, of the other wave. These waves, when they combine, effectively cancel one another out. Depending on the phase relationship between two waves that combine, anything between complete constructive and complete destructive interference is possible.

We’re thinking about waves combining because this resultant waveform, we’re told, is the combination of either this group of waves or this group. Notice something about all of the waves in group one. All of the sets of peaks and all of the sets of troughs line up. Therefore, these waves would interfere constructively, like over here. The resultant waveform would have a clearly defined wavelength. In fact, it would be the same as any one of the waves in this set, except that its amplitude would be several times greater than these waves individually.

Looking now at our actual resultant wave, notice that, number one, its amplitude doesn’t seem to be constant, and number two, that amplitude never gets very much larger than the amplitude of any one of these individual seven or so waves. Because of the irregular displacement of this resultant wave, it’s not likely to have resulted from the addition of all of these waves in group one. This addition, after all, would lead to a much more orderly resultant waveform.

If we look then at group two, we see that these waves are very different from one another. They vary from one another in wavelength, in amplitude, and in phase. When such a variable set of waves are combined together, we would expect to get what we could call an unusual resultant waveform, this one shown in red. This resultant is equal to the sum of many dissimilar waves.

As a side note, all of the waves in group one, because they have the same wavelength and phase and direction relationship, are said to be coherent. This is a characteristic of laser light. However, the waves in group two, which do not have the same wavelength or amplitude or phase, are called incoherent. And this is indeed a characteristic of an incandescent light source. For our answer, we choose group two.

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