Beat Frequency

The video above shows a pair of tuning forks being struck with a mallet. The two forks ring with slightly different frequencies (they are so close that most people likely wouldn’t be able to distinguish one from the other). When we listen to them both simultaneously, though, something interesting happens: we hear periodic oscillations in sound volume, characterized by a signature “wub wub wub” kind of sound. These oscillations in loudness (or “wubs”) are called beats, and they occur with a frequency equal to the difference in frequency between the two distinct notes. Play around with the simulation below to get a feel for why this occurs. Use the sliders to adjust the parameters of the travelling waves in blue and white, and notice what happens to their superposition in red.

To best see the effect, try setting k₁ to 0.08, k₂ to 0.09, the amplitude A to around 100, and the angular frequency ω to any value.