February 27, 2011

Understanding directivity plots

The directivity plots shown in this blog will be unfamiliar to many, but they are not difficult to understand. They are essentially a frequency response plots  which measure from on axis right out to 90 degrees.

Here is one example:

The x axis shows frequency the same as a response plot, but the y axis shows the angle. Think of it this way. Imagine you want to depict a mountain range graphically. You could take a slice through and show a line at that point, but it would only show a small portion of the shape of the mountains. This is very much like a frequency response plot. They only tell part of the story in a very two dimensional way.

If you really wanted to show their shape in one illustration, you might use a contour map. It will have lines where the elevation at each point on the line is the same. It is as if horizontal slices were taken at different heights, and the line is the outline of each slice seen from above. A directivity plot is just like this, but we use SPL instead of elevation.

Interpreting the plot above

The plot above shows an open baffle speaker and I've chosen this one because it includes many of the features you will see with various designs, not normally all in one plot!

Region A - Here you see ideal constant directivity behaviour from 200 - 1k. Dispersion is around 100 degrees. This is very good performance from a small speaker. I don't know of any other type of speaker regardless of size that can control directivity in this way down to 200 Hz. Notice how all the lines are flat at all angles. This means the sound waves that are seen by the room are not altered in tone by the speaker.

Region B - Here the speaker begins to beam from 1 - 2k. This indicates a problem that needs some attention with this design. Ideally we'd like to see a gradual widening in this range, instead of becoming narrow then wider again.

Region C - Again it is constant with a wide dispersion of 150 degrees. Since this only occurs over a restricted range this is a problem. The room will see a little more energy here.

Region D - The most rapid narrowing occurs here then there is a narrowing of response. Above about 9k the tweeter is starting to beam. This is because this speaker used a 3" full range driver.

The most interesting part is the directivity control that comes from an open baffle arrangement.

What does the ideal directivity plot look like?

Something like this would be ideal. True constant directivity from about 200 Hz up to 20k. The ideal dispersion would be about 60 - 90 degrees where the response would be 6 db down. You can find that point by looking at the colour scale, 6db down equates to orange. On the vertical scale, look for 30 degrees off axis to find a total dispersion of 60 degrees.

See more dispersion plot examples on the waveguide shootout page >

Software used

Arta - download >

Arta was used for these plots. The demo version is free to use but saving files is disabled. You can export plots such as these on the demo version.


  1. Nice explanation!

    The speaker was actually a 5" midrange + 1" dome tweeter back to back.


  2. Stupid question: The Sonograms need the registered version of ARTA?

  3. Zog, with the trial version you can generate and export them but not save the orginal files.


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