Monthly Archives: October 2013

Comb filters in acoustics

In this post, I’ll use a feedforward comb filter to explain interference between two sources at some specific location.

The comb filter shows the frequency response of the system. If we have two sources emitting the same signal in space, they will attenuate and amplify certain frequencies at some location according to the frequency response of the comb filter.

The simulation

The red dot represents an ideal microphone in space. Click anywhere inside the simulation to move the sources and the microphone around (you need to click in three separate locations). You can adjust the frequency of the sources using the slider to the right.

How it works

The simulation is done using WebGL shaders, which makes the simulation run really smoothly. The two sources are summed for each pixel in each frame, which gives a nice visual representation of their interference in a 2D plane.

The simulation has the following properties:

  • The sources have identical phases and frequencies.
  • 2000 seconds in the simulation represents 1 second.
  • The size of the box is 1 meter by 1 meter.
  • The sound sources are modeled as cylindrical waves, as per $$\frac{A}{\sqrt{r}}\mathrm{cos}(kr\pm\omega t)$$, with $$A = 1.0$$ for both sources.
  • The initial delay from the nearer source is left out of the diagram of the comb filter, but it could be added without any change in the magnitude of the response.
  • The frequency response for a point is calculated directly from the frequency response of the depicted comb filter.