When two harmonic waves of different frequencies arrive at a point, they produce a characteristic interference signal called beats. The graph on the left represents the value, as a function of time, of the signal resulting from the interference of two waves with the same amplitude. In this important case, the resulting signal can be represented as a harmonic function of time with a frequency equal to the average of the frequencies of each interfering wave, modulated by another harmonic function with frequency equal to one half the difference of the frequencies of the two incoming waves. When the frequencies of the interfering waves are very close to each other, the modulating frequency becomes very small, and the interference signal is often perceived as a fast varying signal with an intensity that changes periodically with time between a low and a high value. The frequency of these changes in intensity is called the beat frequency, and its value is equal to the difference between the frequencies of the two interfering waves.
Question 1: Why is the beat frequency equal to the difference of the frequencies of the two interfering waves, if the frequency of the modulating wave is half that amount? (Click on the graph to toggle the display of the envelope of the signal).
Question 2: Is the signal resulting from the interference a periodic signal? Think carefully before answering.
Question 3: In the limit in which the two interfering waves have the same frequency, the phenomenon of beats should disappear. What happens to the beat frequency in this case? What is the amplitude of the resulting signal?