OpenStax College Physics, Chapter 16, Problem 62 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. Three adjacent keys on a piano are being struck at the same time creating a discord; we have an F, an F sharp and a G with these frequencies 349, 370, and 392 hertz respectively and the question is what beat frequencies are present and so we need to identify all the different pairs of frequencies. So there's an F paired with an F sharp, an F paired with a G and an F sharp paired with a G and so these are three beat frequencies that we will notice. So the first beat frequency will be the absolute value of the difference between the frequency of F and F sharp and these are in no particular order I just called this number one but you could have called any of the other pairs number 1, 2 or 3. So that's 349 minus 370 with you know as a positive that's 21 hertz and then the second beat frequency is the frequency of F minus the frequency of G so it's 349 hertz minus 392 hertz and the absolute value of that is 43 hertz and then the third beat frequency is the difference between the frequency of F sharp and G and that's 370 minus 392 hertz absolute value of which is 22 hertz.