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A simple but very instructive applet which illustrates the topic covered in this Section is provided in by Professor of the ÉîÒ¹ÑÇÖÞ¸£Àû¾Ã¾Ã of Virginia.

The concepts discussed in this section play a very important role in the development of Quantum Mechanics (Chapter 14 of Understanding Physics, particularly Section 14.10).

Note on beats

An examination of Figure 13.43 shows that beats – maxima in the amplitude of the modulating wave (the travelling wave which describes the progress of the envelope modulating the amplitude) – occur at twice the frequency of the modulating wave.

As noted section 13.14, the angular frequency of the modulating wave, ω_b =\( \frac{Δω}{2} \) so that its frequency f_b = \( \frac{Δ´Ú}{2} \) and the beat frequency is

    f = 2 × \( \frac{Δ´Ú}{2} \) = Δ´Ú.

The beat frequency is therefore simply the difference in frequency of two waves.

The beats phenomenon is illustrated in animations from the Massachusetts Institute of Technology and from the Physics Department of the ÉîÒ¹ÑÇÖÞ¸£Àû¾Ã¾Ã of Toronto Beats