In this paper we will argue that the superposition of waves can be calculated in a simple way. We show, using the Gauss’s method to sum an arithmetic sequence, how it is possible to construct the superposition of waves - with different frequencies - in a simple conceptual way. By this method we arrive to the usual result where we can express the superposition of waves as the product of factors, one of them with a cosine function where the cosine’s argument is the average frequency. Most important, we will show that the superposition of waves with slightly different frequencies produces the phase modulation phenomenon as well as the amplitude modulation phenomenon, where we named as phase modulation the phenomenon where there is a phase delay each time that there exits a complete destructive interference. Although this could be a know fact for some physicist (specially those working on the theory of sound), it is important to emphasize this result because, to the best of our knowledge, when studying the superposition of waves with nearly equal frequencies almost all research papers and textbooks only mention that there exist an amplitude modulation.
M. Arevalo Aguilar, L.; Robledo-Sanchez, C.; L. Arroyo Carrasco, M.; and M. M´endez Otero, M.
"The principle of superposition for waves: The amplitude and phase modulation phenomena,"
Applied Mathematics & Information Sciences: Vol. 06:
2, Article 18.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol06/iss2/18