Creating beats with Excel

Many years ago, a friend who is also a physicist like me, visited me and we talked about a few matters. When he told me that he began learning Excel, I knew I could impress him. I told him that I use Excel a lot and added: “Do you want to see how easy it is to create beats with Excel?”.

Beats are a dear and well studied subject among physicists, so his answer was the obvious one.

I opened Excel (here I will provide a screenshot using a much newer version of Excel) and created 4 columns.  The first column contained the numbers 0, 0.1, 0,2 and so on. The first cell of the second column contained the formula = SIN(A1), which I copied down. The first cell of the third column contained the formula = SIN(A1*0.9), which I copied down. The first cell of the fourth column contained the formula = B1+C1, which I copied down.

I considered the first column as containing the angle in radians. I considered the second column as containing the first sine wave. I considered the third column as containing the second sine wave, with a frequency close to the frequency of the first sine wave. I choose 0.9 as the coefficient. I could have chosen 1.1, or 0.09, or 1.01, etc. I considered the fourth column to be the sum of the two sine waves. So, the fourth column represented a beat, because a beat is the sum of two sine waves that have similar (but not exactly equal) frequencies.

For the coefficient and angle step that I chose, I found that with 2000 rows of data, I could nicely get a few periods of the beat.

I plotted each of the second, third, and forth columns, showing my friend each sine wave and the beat. I also plotted them all three in the same graph. At the end, I plotted the two sine waves together and I plotted the beat using the same scale (graph width) underneath the graph of the sine waves. This demonstrated the beat really nicely: My friend was impressed. 