Workout: Beats




the beats simulation on ComPADRE to get some insight into how this works. 

Set up

W. Christian and K. Forinash, © 2017

Pure tone soundwaves are traveling sinusoidal oscillations of air pressure (or, equivalently, density). When they reach your ear, you are measuring the wave at one position. So if it is a pure tone, you will hear a pure oscillation, $y(x,t) = A\sin{(kx-\omega t)}$, at a fixed value of $x$.

Set up the simulation so that both frequencies are equal to 256 Hz. This is middle C on a piano. The screen shows you the density of the air that your ear measures as a function of time. Your screen should look like the image at the right.

Answer these questions

Press the small red speaker button at the middle left bottom of the simulation window to hear the sound. Try a couple of other frequencies (with both frequencies set to the same value) to get a sense of what a range of frequencies sound like. (The note A above middle C is 440 Hz.)

  1. Set the frequencies to 256 and 266. What does the result look like? What does it sound like?
  2. Step the higher frequency down 2 Hz at a time. How the picture change as the frequencies get closer? How does the sound change?
  3. Systematically explore how the differences change the display and the sound result. Does this support what was described in the webpage?


Joe Redish 4/6/18

Article 695
Last Modified: June 10, 2019